Assessing and Characterizing Climate Vulnerabilities in Agriculture-Based Livelihoods: South Sulawesi

1 Introduction

Abstrak

Penghidupan berbasis pertanian kini makin rentan terhadap perubahan iklim, tetapi informasi mengenai potensi resiko dan kebutuhan adaptasi mereka masih sangat terbatas. Bahan ajar ini disusun untuk mengisi kekosongan ini dengan mengevaluasi berbagai jenis kerentanan yang mempengaruhi mata pencaharian berbasis pertanian di tingkat provinsi. Kami melakukan penilaian kerentanan untuk mengidentifikasi risiko utama serta akar penyebabnya, dan potensi adaptasi, dengan fokus pada peningkatan taraf hidup, keberlanjutan produksi komoditas-komoditas kunci, dan pengelolaan lahan secara menyeluruh.

Mengingat keanekaragaman kondisi di masing-masing provinsi, kami memfokuskan perhatian pada kecamatan-kecamatan dengan fitur biofisik dan sosial-ekonomi yang mirip. Ini membantu kami mempermudah tugas dalam mengidentifikasi risiko yang identik antar kecamatan. Kami mendefinisikan area-area homogen ini, atau ‘tipologi,’ dengan menggunakan pengelompokan K-means. Pengelompokan ini didasarkan pada komposit dari indikator biofisik dan sosial-ekonomi. Untuk mempermudah proses pengelompokan, kami menggunakan analisis PCA untuk menyederhanakan dimensi data.

Analisis dibawah ini menunjukkan bagaimana data iklim, ekologi, dan sosial-ekonomi yang dipadukan dengan analisis geospasial dapat membantu memformulasikan kebijakan berbasis bukti. Kebijakan tersebut diharapkan dapat secara tepat menanggulangi berbagai risiko yang berkaitan dengan iklim yang berpotensi mempengaruhi penghidupan berbasis pertanian, serta memungkinkan perancangan strategi adaptasi yang sesuai konteks lokal.

Abstract

Small farmers are increasingly vulnerable to climate change, yet little is known about their specific risks and adaptation requirements. Our study aims to address this gap by examining the different vulnerabilities affecting agriculture-based livelihoods at the provincial level. We conducted climate vulnerability assessments to identify key risks and their root causes, as well as possible mitigation measures, with a focus on sustaining livelihoods, key commodities production, and overall land management.

Considering the diverse conditions of the study area, we narrowed our focus to locations with similar biop hysical and socio-economic features. This helped us streamline the task of spotting common risks across communities. We defined these homogeneous areas, or ‘typologies,’ using K-means clustering. The clustering was based on a composite of biophysical and socio-economic indicators. To make the clustering process more precise, we applied PCA analyses to simplify the data dimensions.

Our analysis underscores the value of geospatial tools and socio-economic data in shaping evidence-based policies. These policies can aptly tackle a spectrum of climate-related risks affecting agriculture-based livelihoods, enabling the design of targeted adaptation measures.

Objective

We aimed to identify homogeneous areas, or ‘typologies’, with similar biophysical and socio-economic features within the diverse study area, using K-means clustering on PCA-simplified data to infer common risks across South Sulawesi Province.

1.1 Pipeline

A flowchart includes steps in performing PCA.

1.2 Loading the data

Reading the Data: We have an Excel file with lots of information. Each row in the file gives us details about a village, and the columns tell us about different factors that might make the village more or less vulnerable to climate change. There’s also a special sheet in the Excel file that explains what all these factors mean, their unique IDs, and how they’re measured.

1.2.1 The main dataset raw_df

Code

library(readxl)
library(dplyr)
library(corrplot)
library(caret)
library(gtExtras)
library(naniar)
library(knitr)
library(kableExtra)

df_raw <-
  read_xlsx("data/analisa_tipologi_sulsel.xlsx",
            sheet = "fin_copas") |> 
  janitor::clean_names() |> dplyr::select(-c(idkec_2, idkec_3)) |> 
  mutate(across(-c(idkec_dum, sumber, nmprov, nmkab, nmkec), as.numeric))

Code

# Select a subset of columns for clarity
df_selected <- df_raw|>
  dplyr::select(1,7,8,10,11, 12) |> head()

# Create the table using gt
df_selected|>
  gt()|>
  tab_header(
    title = "A sample of the Data"
  )|>
  cols_label(
    idkec_dum = "ID",
    nmkab = "District",
    nmkec = "Sub-district",
    distance_to_plantation = "Dist. to Plantation (m)",
    distance_to_road = "Dist. to Road (m)",
    distance_to_commodity_processing_factory = "Dist. to Comm.Proc Factory (m)"
  )|>
  fmt_number(
    columns = c(distance_to_plantation, distance_to_road, distance_to_commodity_processing_factory),
    decimals = 2
  )

A sample of the Data
ID	District	Sub-district	Dist. to Plantation (m)	Dist. to Road (m)	Dist. to Comm.Proc Factory (m)
7301010a	KEPULAUAN SELAYAR	PASIMARANNU	221,140.99	3,151.66	295,618.47
7301011a	KEPULAUAN SELAYAR	PASILAMBENA	268,465.24	1,996.38	355,496.81
7301020a	KEPULAUAN SELAYAR	PASIMASSUNGGU	184,133.49	1,649.59	251,716.26
7301021a	KEPULAUAN SELAYAR	TAKABONERATE	163,497.97	4,252.98	242,261.12
7301022a	KEPULAUAN SELAYAR	PASIMASSUNGGU TIMUR	188,167.82	861.54	258,492.26
7301030a	KEPULAUAN SELAYAR	BONTOSIKUYU	99,706.86	744.58	173,876.77

Now we have a big table called df_raw. This table contains information like the name of the province, district, sub-district, and village. It also includes data about the village’s area, population density, and lots of other numerical factors.

Code

# Remove unnecessary columns from the original dataframe 'df_raw'
# The 'dplyr::select()' function is used to exclude these columns
df_gt <- df_raw |> 
  dplyr::select(-c(idkec_dum, kdprov, sumber, nmprov, nmkab, nmkec, periode, kdkab, kdkec, prec_change))

df_col_unstandardise <- df_raw |> dplyr::select(prec_change)

# Add a small constant (0.001) to every value in 'df_gt'
# This is often done to allow for log transformations of data that includes zeros
df_gt_plus <- df_gt + 0.001



# Log-transform and scale the data
# 1. 'as_tibble()' converts the dataframe to a tibble for easier manipulation
# 2. 'mutate_all(.funs = log10)' applies the base-10 logarithm to all columns
# 3. 'scale()' standardizes each column so that it has mean=0 and sd=1
scaled_df <-
  df_gt_plus |> as_tibble() |> mutate_all(.funs = log10) |> bind_cols(df_col_unstandardise) |>  scale(center = TRUE, scale = TRUE)

# Add back the columns that were removed earlier to create a complete, scaled dataframe
# 'bind_cols()' binds the selected columns from 'df_raw' and the scaled columns from 'scaled_df'
scaled_df_complete <- df_raw |> 
  dplyr::select(c(idkec_dum, kdprov, sumber, nmprov, nmkab, nmkec, periode, kdkab, kdkec)) |>  
  bind_cols(scaled_df)

# Remove the column 'korban_jiwa_kebakaran_hutan_dan_lahan_2018_2019' from the complete, scaled dataframe
scaled_df_complete_temp <- scaled_df_complete |> 
  dplyr::select(-korban_jiwa_kebakaran_hutan_dan_lahan_2018_2019)

2 Preparing the data

Before diving into the PCA, let’s ensure that the data meets the necessary requirements.

2.1 Check for missing values

Code

# Check for missing values
missing_data <- sapply(scaled_df_complete_temp, function(x) sum(is.na(x)))

# print missing data\
scaled_df_complete_temp|> filter_all(any_vars(is.na(.))) |>   dplyr::select("ID Kecamatan" = 1, "Nama Kabupaten" = 5, "Nama Kecamatan " = 6) |> kable(caption = "Kecamatan dengan data tidak lengkap")

Kecamatan dengan data tidak lengkap

ID Kecamatan	Nama Kabupaten	Nama Kecamatan
7313000a	WAJO	WAJO
7322011a	LUWU UTARA	SABBANG SELATAN
7322021a	LUWU UTARA	BAEBUNTA SELATAN
7322041a	LUWU UTARA	SUKAMAJU SELATAN
7325000a	LUWU TIMUR	LUWU TIMUR
7371081a	MAKASSAR	KEPULAUAN SANGKARRANG

Code

#remove missing data
scaled_df_complete_temp <- scaled_df_complete_temp[complete.cases(scaled_df_complete_temp), ]

2.2 Exclude identifiers

Code

df_pre_pca <- scaled_df_complete_temp |> 
  select(-c(idkec_dum, sumber, kdprov, nmprov, nmkab, nmkec, periode, kdkab, kdkec))

glimpse(df_pre_pca) |> kbl(caption = "Input data for a PCA Analysis") |>   kable_paper()|>
  scroll_box(width = "1000px", height = "500px")

Rows: 306
Columns: 49
$ distance_to_plantation                                                      <dbl> …
$ distance_to_road                                                            <dbl> …
$ distance_to_commodity_processing_factory                                    <dbl> …
$ distance_to_plantation_concession                                           <dbl> …
$ distance_to_forest                                                          <dbl> …
$ distance_to_river                                                           <dbl> …
$ distance_to_burned_area                                                     <dbl> …
$ percentage_of_agricultural_area_small_holder_in_the_village                 <dbl> …
$ percentage_of_plantation_area_per_sub_district                              <dbl> …
$ percentage_of_forested_area_in_the_sub_district                             <dbl> …
$ percentage_of_shrubland_in_the_sub_district                                 <dbl> …
$ percentage_of_water_area_compared_to_sub_district_area                      <dbl> …
$ distance_to_deforestation                                                   <dbl> …
$ percentage_deforestation_area_size                                          <dbl> …
$ arable_land_percent                                                         <dbl> …
$ erosion_risk_t_ha_1_yr_1                                                    <dbl> …
$ indeks_bahaya_banjir                                                        <dbl> …
$ indeks_bahaya_longsor                                                       <dbl> …
$ buffer_to_500m_irigated_land                                                <dbl> …
$ aridity_index                                                               <dbl> …
$ total_kk_berdasarkan_pengguna_dan_non_pengguna_listrik                      <dbl> …
$ rasio_elektrifikasi                                                         <dbl> …
$ rasio_sekolah_tinggi_sma_sederajat                                          <dbl> …
$ rasio_pt                                                                    <dbl> …
$ rasio_rs                                                                    <dbl> …
$ rasio_faskes_1                                                              <dbl> …
$ rasio_pasar                                                                 <dbl> …
$ rasio_minimarket_swalayan                                                   <dbl> …
$ banyak_kejadian_tanah_longsor_2018_2019                                     <dbl> …
$ korban_jiwa_tanah_longsor_2018_2019                                         <dbl> …
$ banyak_kejadian_banjir_2018_2019                                            <dbl> …
$ korban_jiwa_banjir_2018_2019                                                <dbl> …
$ banyak_kejadian_banjir_bandang_2018_2019                                    <dbl> …
$ korban_jiwa_banjir_bandang_2018_2019                                        <dbl> …
$ banyak_kejadian_kebakaran_hutan_dan_lahan_2018_2019                         <dbl> …
$ banyak_kejadian_kekeringan_lahan_2018_2019                                  <dbl> …
$ korban_jiwa_kekeringan_lahan_2018_2019                                      <dbl> …
$ jumlah_sistem_peringatan_dini_bencana_alam                                  <dbl> …
$ persentase_sistem_peringatan_dini_bencana_alam                              <dbl> …
$ rasio_embung_di_kecamatan                                                   <dbl> …
$ rasio_pasar_desa_pasar_hewan_pelelangan_ikan_pelelangan_hasil_pertanian_dll <dbl> …
$ jumlah_warga_penderita_gizi_buruk_marasmus_dan_kwashiorkor_pada_tahun_2018  <dbl> …
$ rasio_warga_penderita_gizi_buruk_marasmus_dan_kwashiorkor_pada_tahun_2018   <dbl> …
$ annual_mean_temp                                                            <dbl> …
$ temp_change                                                                 <dbl> …
$ annual_mean_prec                                                            <dbl> …
$ rasio_40pers_ekon_rendah_rt                                                 <dbl> …
$ rasio_40pers_ekon_rendah_indv                                               <dbl> …
$ prec_change                                                                 <dbl> …

Input data for a PCA Analysis

distance_to_plantation	distance_to_road	distance_to_commodity_processing_factory	distance_to_plantation_concession	distance_to_forest	distance_to_river	distance_to_burned_area	percentage_of_agricultural_area_small_holder_in_the_village	percentage_of_plantation_area_per_sub_district	percentage_of_forested_area_in_the_sub_district	percentage_of_shrubland_in_the_sub_district	percentage_of_water_area_compared_to_sub_district_area	distance_to_deforestation	percentage_deforestation_area_size	arable_land_percent	erosion_risk_t_ha_1_yr_1	indeks_bahaya_banjir	indeks_bahaya_longsor	buffer_to_500m_irigated_land	aridity_index	total_kk_berdasarkan_pengguna_dan_non_pengguna_listrik	rasio_elektrifikasi	rasio_sekolah_tinggi_sma_sederajat	rasio_pt	rasio_rs	rasio_faskes_1	rasio_pasar	rasio_minimarket_swalayan	banyak_kejadian_tanah_longsor_2018_2019	korban_jiwa_tanah_longsor_2018_2019	banyak_kejadian_banjir_2018_2019	korban_jiwa_banjir_2018_2019	banyak_kejadian_banjir_bandang_2018_2019	korban_jiwa_banjir_bandang_2018_2019	banyak_kejadian_kebakaran_hutan_dan_lahan_2018_2019	banyak_kejadian_kekeringan_lahan_2018_2019	korban_jiwa_kekeringan_lahan_2018_2019	jumlah_sistem_peringatan_dini_bencana_alam	persentase_sistem_peringatan_dini_bencana_alam	rasio_embung_di_kecamatan	rasio_pasar_desa_pasar_hewan_pelelangan_ikan_pelelangan_hasil_pertanian_dll	jumlah_warga_penderita_gizi_buruk_marasmus_dan_kwashiorkor_pada_tahun_2018	rasio_warga_penderita_gizi_buruk_marasmus_dan_kwashiorkor_pada_tahun_2018	annual_mean_temp	temp_change	annual_mean_prec	rasio_40pers_ekon_rendah_rt	rasio_40pers_ekon_rendah_indv	prec_change
2.6922633	1.7166810	2.0357668	-4.3825590	-0.6076871	2.7117976	3.3492440	-2.0718191	-1.0500575	1.3812193	-0.2416110	-0.1655192	-0.8987080	1.4974779	0.0159813	-1.3634738	0.0658418	0.0690122	-0.7093641	-2.8351594	-0.8784002	0.3900809	-0.8662722	-0.5335278	-0.4631427	-0.9351701	16.7717433	-1.4290972	-0.7849217	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-0.2706541	-0.8396838	-1.2024273	1.1710368	-0.9072150	-0.9131378	0.1837850	0.0129179	-0.1064804	-0.2500750	-1.0432363	0.1491026
2.9183618	1.2690894	2.2307442	-4.3825590	0.3766393	3.9039885	3.5942067	-0.3934067	-0.7356651	-0.3764903	-0.2416110	-0.1655192	0.1012585	0.3936954	0.5254928	-1.0656104	-2.0115443	0.0794378	-0.7093641	-4.2911316	-1.5251892	-0.3590277	-0.3356609	-0.5335278	-0.4631427	-1.0861552	0.5143758	-1.4290972	-0.7849217	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-0.9894272	-1.1001485	-1.2024273	-0.7813405	-0.9072150	-0.9131378	0.1859142	0.0214586	-0.1515203	1.1414194	0.9709774	0.1881462
2.4787354	1.0820430	1.8658209	-4.3825590	-1.1584093	1.7751776	3.1240451	-2.9534347	-1.2100183	1.3370173	-0.2416110	-0.1655192	-1.6426342	1.9354174	-0.0945629	-0.9964380	-0.5942738	0.5340932	-0.7093641	-2.3585071	-1.3525855	0.4722171	-0.4940463	-0.5335278	-0.4631427	-0.9692783	0.2031787	0.6897151	-0.7849217	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-0.6042839	-1.1638023	0.5072149	1.2216349	-0.9072150	-0.9131378	0.1772192	0.0014243	-0.0865877	0.8205483	0.6070416	0.0998882
2.3401524	2.0104617	1.8253486	-4.3825590	1.9776268	2.6743789	3.0626712	-3.1684987	0.8594398	-1.1028887	-0.2416110	-0.1655192	2.2341680	-0.9107321	0.2493056	-1.0585105	-2.0115443	-0.0698078	-0.7093641	-3.1873771	-0.6296110	0.4722171	-1.0280983	-0.5335278	-0.4631427	-0.7667049	-0.0188810	-1.4290972	-0.7849217	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	0.0236306	-0.7517573	-1.2024273	-0.7813405	0.9734290	1.0648922	0.1975911	0.0804964	-0.1035534	0.2970001	0.1627442	-0.3776906
2.5040049	0.4452930	1.8939007	-4.3825590	-1.1970300	0.7241760	3.1609066	0.2804503	-1.3357507	1.1498652	-0.2416110	-0.1655192	-1.7422677	1.2423341	0.2617237	-0.6945947	0.1759761	0.4057864	-0.7093641	-2.2521679	-1.5811049	0.4722171	-0.2815524	-0.5335278	-0.4631427	-1.1240181	0.2873801	-1.4290972	-0.7849217	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-1.2068218	-1.0157277	-1.2024273	-0.7813405	0.9734290	0.9767542	0.1839826	0.0613235	-0.0866315	1.0480802	0.6995387	-0.2048771
1.7635225	0.3022711	1.4747432	-4.3825590	0.3508672	3.5339007	2.5478689	-0.8775240	-1.0451284	-0.1403128	-0.2416110	-0.1655192	0.2548015	0.5129857	0.4739327	-0.5793101	-0.6267548	0.7363484	-0.7093641	-1.7343654	-0.4647902	0.4515612	-0.3728164	-0.5335278	-0.4631427	-1.1394242	0.4966298	-1.4290972	-0.7849217	-0.1128779	0.5193370	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	0.7424211	-1.0542972	0.8894775	1.1148349	0.9734290	1.0801597	0.1647237	-0.0131299	-0.0583580	-0.0143037	-0.3588968	-0.6911786
1.5156237	-0.0129617	1.3754048	-4.3825590	0.1491911	3.4102418	2.3802827	0.1371349	-0.7239240	0.1028039	-0.2416110	2.8435806	-0.0833787	-0.1179987	0.5782899	-0.6121307	-0.2118106	0.6487932	-0.7093641	-1.6466687	-0.7011528	0.4722171	0.5707859	-0.5335278	2.0465777	-0.9326452	-0.2190505	-1.4290972	0.9300293	-0.1128779	0.6772291	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-0.4319047	-0.5215700	0.9255706	1.2818974	0.8020628	1.1528553	0.1720294	-0.0345229	-0.0517680	0.2567754	0.0656445	-0.8134475
1.4488294	-1.6311223	1.3488266	-4.3825590	-0.6259825	3.3446595	2.3333130	-3.1684987	1.7639449	-0.6764544	-0.2416110	-0.1655192	-0.7970139	-0.9107321	0.1595843	-0.5319471	0.5520886	0.2575397	-0.7093641	-2.0509075	0.0056923	0.4722171	0.6323259	-0.5335278	-0.4631427	1.7378697	-0.0287617	0.6227789	-0.7849217	-0.1128779	0.6772291	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-2.7211713	1.8809765	-1.2024273	-0.7813405	1.2451515	0.9738194	0.1826832	-0.1316233	-0.0669647	-1.5416374	-1.5338714	-0.6054536
1.3652535	-0.3441120	1.3402592	-4.3825590	0.5954391	3.2691351	2.3116250	0.0554156	-1.7906651	-0.9116556	-0.2416110	-0.1655192	0.9652386	-0.9107321	0.6176875	-0.4305199	-0.3590581	0.7658135	-0.7093641	-1.2549489	-0.6685860	0.3454874	-0.1724110	-0.5335278	-0.4631427	-1.1107751	0.3298266	-1.4290972	1.3293395	-0.1128779	0.5193370	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	0.2868788	-0.9786007	0.7938533	1.1904462	-0.9072150	-0.9131378	0.1605713	-0.0125327	-0.0264401	0.0097552	-0.2052716	-0.9307801
0.9956777	-0.4693720	1.2338968	-4.3825590	1.3251927	2.8980590	2.1182421	0.1471251	-0.4557314	-1.1028887	-0.2416110	-0.1655192	1.6068811	-0.9107321	0.5490962	-0.9215756	-0.3227730	0.0041250	-0.7093641	-1.4285871	-0.4893694	0.2474277	-0.3496292	-0.5335278	-0.4631427	-0.7892380	0.7109696	-1.4290972	1.2025710	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	0.6360828	-1.0097682	-1.2024273	-0.7813405	-0.9072150	-0.9131378	0.1770299	0.0193866	-0.0326599	0.6140433	0.1761475	-1.0610479
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1.1052359	-0.2862466	-1.4975538	0.0671787	0.1768856	-1.8991883	0.0177658	0.2649183	-0.2276213	-0.2363715	-0.2416110	-0.1655192	-0.1065306	-0.7570370	-0.1310396	-1.4842718	1.2112895	-1.5361490	1.8688971	0.6600305	-0.0406418	0.4722171	1.0851941	-0.5335278	-0.4631427	0.6105541	-0.3098221	0.6597182	-0.7849217	-0.1128779	1.1779948	4.5028379	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-0.7894422	0.4962618	-1.2024273	-0.7813405	1.6592724	0.7410894	0.1904489	0.1416166	0.2258602	0.7292854	0.9786102	0.1868181
1.0446522	-0.0136502	-2.1505165	0.0785289	0.1302537	-0.5960238	0.2090842	0.4632836	0.1836177	-0.3230007	-0.2416110	-0.1655192	-0.2356120	0.0535965	0.1248362	-0.5745370	1.0883372	-1.5361490	1.9767846	0.6606270	0.5535163	0.4687688	-0.7303157	-0.5335278	-0.4631427	1.0128834	-0.0598623	0.6442183	-0.7849217	-0.1128779	1.0657407	-0.2161285	2.9413631	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-0.6042839	1.0627887	-1.2024273	1.2090360	0.8020628	1.2690767	0.1877168	0.1452051	0.2261440	-0.9392196	-0.8128572	0.2524100
1.0183739	-0.8043037	-1.3195287	-0.0440454	0.4745114	-1.3697861	-0.6304782	0.6415063	1.3252214	-1.1028887	-0.2416110	-0.1655192	0.4173160	-0.9107321	0.3361134	-1.1485087	1.1461364	-1.5361490	1.9118243	0.6735897	0.9943363	0.4722171	2.0572850	1.7771501	2.2373646	1.3113811	-0.0864659	0.4948966	-0.7849217	-0.1128779	1.0855736	4.5028379	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-0.6042839	1.5777284	-1.2024273	-0.7813405	1.2451515	1.0653986	0.1926225	0.1203266	0.2201068	-1.4964843	-1.2957401	-0.1260634
1.0445868	-0.1538384	-1.1030953	0.0758228	0.0633569	-1.4485418	-0.0967376	0.5157531	0.7456799	-1.1028887	-0.2416110	-0.1655192	-0.2043741	-0.9107321	0.0482348	-1.7247356	1.2228867	-1.5361490	-0.0975147	0.6646141	0.1365442	0.4722171	1.7679220	1.9388213	-0.4631427	1.1350133	-0.1874557	0.5549072	-0.7849217	-0.1128779	1.0657407	-0.2161285	2.9413631	6.2819793	-0.2945872	-0.3663205	-0.0567962	-0.9894272	0.8409862	0.9072276	-0.7813405	1.3163159	0.9466819	0.1918835	0.1473281	0.2240567	0.3625931	0.5082090	0.0033467
1.0193461	-0.4709592	-0.8071651	0.1161151	-0.0061888	-1.7696296	0.0263051	0.0890782	-0.4208332	0.6949008	-0.2416110	-0.1655192	-0.3221691	0.9698742	-0.4582505	-0.3862392	1.1759811	0.0812329	-0.7093641	0.6286913	0.3917231	-0.0596377	0.1453456	-0.5335278	-0.4631427	0.3937430	-0.1198934	0.7020283	-0.7849217	-0.1128779	1.1207102	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	0.0236306	0.4413023	-1.2024273	-0.7813405	0.9734290	1.1594996	0.1903044	0.1322515	0.2265789	0.4553071	0.6689750	-0.0324220
0.7704941	0.5328297	-0.6678449	-0.1313684	-1.2239327	0.1439709	-0.6248616	0.3780345	-0.1120158	1.3725874	-0.2416110	-0.1655192	-1.4780712	1.4751380	-0.0804973	-0.1064845	0.6186297	0.7680772	1.2580375	0.4821103	0.4711295	0.4357308	0.6736436	-0.5335278	-0.4631427	0.6701133	-0.0393987	0.6683254	-0.7849217	-0.1128779	1.1649661	4.9329899	2.9413631	6.2819793	-0.2945872	2.5035881	-0.0567962	-0.6042839	0.9665493	0.9406825	-0.7813405	0.8020628	1.2614452	0.1631283	0.0540698	0.1904805	-0.1756146	-0.0709090	-0.3076041
0.7698528	-0.0461416	-0.7452556	-0.3467252	-1.6296588	-0.3639810	-1.3432009	0.3279562	-0.2403203	1.3633885	-0.2416110	-0.1655192	-1.6116734	1.3251804	0.0726554	-0.1227481	0.6327097	0.5748005	1.2090269	0.3583425	0.1976421	0.2960964	0.3809274	-0.5335278	-0.4631427	0.7719061	-0.1983201	0.6830360	1.2739612	-0.1128779	1.2020110	-0.2161285	-0.3002999	-0.1390876	-0.2945872	3.3115666	-0.0567962	-0.9894272	0.9123570	-1.2024273	1.3650428	-0.9072150	-0.9131378	0.1608505	0.0759823	0.1693537	0.4511824	0.4831891	-0.2964140
0.9880977	-0.5850159	-1.2931888	-0.3829968	0.0104025	-0.4319388	-1.1199741	0.3878806	0.1017369	-0.3471058	-0.2416110	-0.1655192	-0.3740956	-0.3601765	0.5617630	-0.1339702	0.7610361	-0.0027857	1.5905974	0.4142253	0.4047341	0.4722171	-0.2254989	-0.5335278	-0.4631427	0.2206752	-0.1226806	0.6618281	-0.7849217	-0.1128779	0.7696186	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-0.2706541	0.6591948	-1.2024273	1.2344786	-0.9072150	-0.9131378	0.1817268	0.1164738	0.1785964	-0.1431911	-0.1855945	-0.0725478
0.7369377	0.5642957	-0.4810215	-0.5984845	-1.2639808	-0.0118443	-1.0155203	-0.3244609	-1.1629855	1.2265724	-0.2416110	-0.1655192	-1.2239534	0.5184238	0.1460869	0.3867002	-0.1673132	0.7751630	0.1868859	0.3897232	-0.3489272	-8.7305008	0.6676447	-0.5335278	-0.4631427	0.1148188	0.5474337	-1.4290972	0.9300293	-0.1128779	0.8351781	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-0.4319047	-0.1101217	0.7989589	1.3144810	-0.9072150	-0.9131378	0.1168833	0.0525847	0.1570478	0.9694389	0.9491939	-0.3307362
0.0197808	0.5989323	-0.0039672	-0.5663583	-1.3665159	-0.1079565	0.5397642	-0.2877017	-0.6689654	1.1467954	-0.2416110	-0.1655192	-1.9606342	1.2318910	0.2440003	0.6967468	-0.4279688	0.7283702	-0.7093641	0.6091168	-0.6370987	-0.6227070	0.4863106	-0.5335278	-0.4631427	1.3026090	0.1623349	0.6013504	0.9300293	-0.1128779	0.9275866	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-0.2706541	-0.5578106	0.8298717	-0.7813405	-0.9072150	-0.9131378	0.0737230	0.1546532	0.1824022	0.3364133	0.0279424	-0.9513548
0.5103783	0.7611395	0.5723362	0.2959410	-0.6642086	-0.3994003	-0.4911821	0.3785485	-1.3482142	1.1455092	-0.2416110	-0.1655192	-0.9439898	0.9938712	0.1471852	0.4138851	0.6118605	0.5852279	0.5908708	0.2035972	-0.5023282	-0.9219664	0.3152728	1.8705656	-0.4631427	0.7024060	-0.0513391	0.6729922	1.2739612	-0.1128779	0.7696186	-0.2161285	-0.3002999	-0.1390876	3.3975921	2.7913150	-0.0567962	-0.7894422	-0.0430522	0.8433473	-0.7813405	1.2832837	0.9057248	0.1247044	0.0832092	0.1326641	0.8700931	0.7100586	-0.9001727
-0.0300048	0.7888970	0.2199620	-0.0776991	-0.4492820	-0.0701048	0.6576203	-0.5657865	-1.1626789	1.1986755	-0.2416110	-0.1655192	-0.6399085	0.1940620	0.2377659	0.5520123	-1.2167867	0.8547074	-0.7093641	0.5826615	-0.7090142	-0.2346037	-0.9787628	-0.5335278	-0.4631427	-0.3516118	0.1869775	0.7526934	0.9300293	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	-0.2945872	2.5035881	-0.0567962	0.5250170	-1.1898459	0.6608507	-0.7813405	0.8020628	1.1521271	0.0767891	0.1894652	0.1741378	0.5716621	0.2809048	-1.0794044
2.7247421	1.3450365	1.9530508	-4.3825590	0.3446379	4.5902009	3.3387840	0.0586358	-0.4825502	1.1963227	-0.2416110	-0.1655192	0.1655223	1.5380296	-0.3631097	-1.7423764	-0.1357881	-1.5361490	-0.7093641	-3.2766023	0.0371378	-3.8219247	-0.2813196	-0.5335278	-0.4631427	-0.4327184	-0.4902254	-1.4290972	-0.7849217	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	0.0236306	0.0270973	-1.2024273	-0.7813405	-0.9072150	-0.9131378	0.1930034	0.0275292	-0.1527536	0.5692211	0.6038913	0.5984210
2.2533930	2.2976088	1.5224896	0.3010379	0.0577220	4.2280164	3.0282453	-0.5068261	-0.5468146	1.2107105	-0.2416110	-0.1655192	0.7233521	1.7719558	-0.1055768	-0.6429553	0.4670596	-1.5361490	-0.7093641	-0.7726840	-0.5901857	-0.2866240	1.9960486	-0.5335278	-0.4631427	-0.9626089	-0.4902254	-1.4290972	-0.7849217	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	3.0611569	-0.3663205	-0.0567962	-0.6042839	-0.2732147	-1.2024273	-0.7813405	-0.9072150	-0.9131378	0.1906945	-0.0366275	0.0490877	1.0199290	1.0146312	0.3046417
1.3808487	1.6865232	0.0780973	0.4387473	1.9492583	2.6835017	1.4963402	-3.1684987	1.4556399	-1.1028887	-0.2416110	-0.1655192	2.2391513	-0.9107321	-4.4973391	-8.3073542	-2.0115443	-1.5361490	-0.7093641	-3.4995135	-0.3132502	0.4722171	0.0904002	-0.5335278	-0.4631427	-0.7750846	-0.4902254	-1.4290972	-0.7849217	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	0.0236306	-0.3822044	-1.2024273	-0.7813405	-0.9072150	-0.9131378	-7.7955680	-7.8028518	-7.7819186	1.0026278	1.2472649	1.1056816
1.3478521	1.2203379	-0.1042381	0.3341945	-0.0863422	1.2846306	0.3271836	-3.1684987	1.5119650	0.9766283	-0.2416110	-0.1655192	0.0749847	2.2647285	-4.4973391	-8.3073542	-2.0115443	-1.5361490	-0.7093641	-1.6281694	-0.6590308	0.4722171	2.5484432	-0.5335278	-0.4631427	-1.1043049	-0.4902254	-1.4290972	-0.7849217	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-0.6042839	-0.3536354	0.8276787	-0.7813405	1.2000520	0.9371258	-7.7955680	-7.8028518	-7.7819186	0.5852573	0.6514599	1.1056816
1.0914929	0.0871439	-0.5689174	0.1838176	0.3335444	-1.8323062	-0.6001288	0.2614465	0.8201151	-1.1028887	-0.2416110	-0.1655192	0.0281460	-0.9107321	-0.2018539	0.0848185	1.2270370	-1.5361490	-0.7093641	0.7723230	1.0702304	0.4722171	0.7664629	1.7852585	2.2459047	0.1617271	-0.4902254	0.6684984	0.9300293	-0.1128779	1.0855736	-0.2161285	-0.3002999	-0.1390876	-0.2945872	2.5035881	-0.0567962	0.0236306	1.2338939	1.2047934	-0.7813405	0.8020628	1.3169406	0.1907839	0.1410480	0.2484096	-1.2267508	-0.9783760	0.0429058
0.9261104	0.2793468	-0.4059476	0.1059529	-1.2929589	-0.0328600	-0.6951686	0.2527627	0.2359393	1.2732282	-0.2416110	-0.1655192	-1.6754119	1.1223453	-0.1772631	0.2933324	0.7765312	0.8140821	-0.7093641	0.6656505	0.8145105	0.2315376	0.4776621	-0.5335278	-0.4631427	0.6800300	-0.2017209	0.5850207	-0.7849217	-0.1128779	0.7696186	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-0.2706541	1.1378710	0.9421468	-0.7813405	0.9734290	1.1986628	0.1705929	0.0904033	0.2267059	-0.5816577	-0.3656763	-0.2526418
0.5919765	0.2960747	-0.3211731	-0.2141745	-2.6452932	0.6662508	0.2411965	0.0100518	-0.8719921	1.4015828	-0.2416110	-0.1655192	-2.4261980	1.7599350	-0.3577963	0.3536311	-0.0138127	0.9010619	-0.7093641	0.5535250	-0.3585267	0.0206010	0.1426633	-0.5335278	-0.4631427	-0.2961603	0.0731802	0.6870643	1.2025710	-0.1128779	0.5193370	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-1.4449486	0.5764328	0.6731885	-0.7813405	1.1448570	0.9954130	0.1213328	0.0843522	0.1924850	-0.1019808	-0.1384383	-0.4520095
0.5769548	0.3207810	-0.1386452	-0.0855457	-1.8719420	-0.2470830	0.3420355	-0.0630626	-0.9718122	1.3003274	-0.2416110	-0.1655192	-1.6934080	1.6225645	-0.3177635	0.4862831	-2.0115443	0.8643687	-0.7093641	0.4591683	-0.9384104	0.1285391	0.1224043	-0.5335278	-0.4631427	-0.6888235	-0.1775967	-1.4290972	1.2025710	-0.1128779	0.6772291	-0.2161285	3.2663609	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-2.7211713	0.7781318	0.5297973	1.2599493	-0.9072150	-0.9131378	0.1329736	0.0973084	0.1832756	1.0826104	0.8522660	-0.3892172
0.9810375	-0.1997016	-0.2039209	0.1750888	-0.2711437	-0.8255880	-0.7314292	0.2281338	0.2371719	0.9597573	-0.2416110	3.7431920	-0.6597539	1.2635831	0.0939971	0.2035743	0.7875167	0.3763836	-0.7093641	0.6834407	0.9959477	0.2028977	0.2500967	-0.5335278	2.2375459	0.3340280	-0.0207358	0.7611563	0.9300293	-0.1128779	0.9931555	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-0.2706541	1.3498152	0.9931586	1.2891704	-0.9072150	-0.9131378	0.1738094	0.1198063	0.2345255	-0.5559219	-0.4754746	-0.2749981
1.1090238	-0.4364730	-0.1900746	0.2342802	0.2584079	-0.4694867	-1.1472182	0.2519935	-0.4688049	-1.1028887	-0.2416110	-0.1655192	0.2209780	-0.9107321	0.2606848	0.2560352	1.0333673	-0.4628318	-0.7093641	0.8087245	1.3539251	0.4080616	-1.2292245	-0.5335278	2.2778278	0.0921024	-0.1626750	0.8546406	-0.7849217	-0.1128779	0.8860332	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	0.9424141	0.9324680	0.9094988	-0.7813405	-0.9072150	-0.9131378	0.1873097	0.1448444	0.2613249	0.1507475	0.1906638	-0.1204823
1.1160430	-0.6252732	-0.0095218	0.2615266	0.1606893	0.8431288	-1.3587443	-0.0090017	-0.7202290	-0.6702408	-0.2416110	-0.1655192	0.3289056	-0.9107321	0.2211164	0.2631441	1.0244331	-0.4651733	-0.7093641	0.7989678	0.8661395	0.4024162	-0.6429366	-0.5335278	-0.4631427	0.0235287	-0.2964231	0.8069071	-0.7849217	-0.1128779	0.6772291	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	0.1587199	0.9024422	0.8183487	-0.7813405	0.9734290	1.2034453	0.1857227	0.1340117	0.2626646	-0.0807133	-0.0457571	-0.2019309
1.0901771	-0.4716106	0.1215677	0.2660490	-0.0226820	0.8162628	-1.0381779	0.4377828	-0.3621691	0.3437680	-0.2416110	-0.1655192	0.2120464	-0.9107321	0.2284028	0.3141033	0.8850796	0.0565959	-0.7093641	0.7056707	0.1539788	0.4495969	-0.3928223	-0.5335278	-0.4631427	-0.1028974	-0.1905914	0.6787633	-0.7849217	-0.1128779	1.0200015	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-0.9894272	0.8613522	0.8761008	-0.7813405	0.9734290	1.1374770	0.1781023	0.0874681	0.2444194	-0.1865266	-0.2287267	-0.4105586
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0.5479931	1.5996572	1.0546066	0.3126839	1.4268487	0.0491545	0.1148625	-1.5128687	-0.3055450	-1.1028887	5.6170694	1.9898242	1.6955342	-0.9107321	-2.1975791	-1.7921787	0.6648735	-1.5361490	-0.1482289	-1.2590657	0.5880687	0.4722171	0.2308868	1.8779640	1.9618372	1.0362803	-0.0682139	0.5213883	-0.7849217	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-0.2706541	0.8733553	-1.2024273	-0.7813405	1.0737029	1.1223556	0.1834027	0.1540004	-0.0262824	-3.9841991	-3.8843240	-0.3112211
0.6958488	-3.7152365	-1.7272627	0.1615486	-0.1395004	-0.1759621	-0.2111284	-3.1684987	2.2234056	-1.1028887	-0.2416110	-0.1655192	-0.5094004	-0.9107321	-4.4973391	-0.3007111	0.9606534	-1.5361490	-0.7093641	0.7124836	1.0472000	0.4722171	1.5005225	1.8631988	2.1284073	0.2512365	0.1930706	0.5161044	-0.7849217	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	0.7424211	0.7119164	-1.2024273	-0.7813405	1.1448570	1.1256271	0.1939543	0.1587459	0.2188705	-1.4861999	-1.2022213	0.4398175
0.7295890	-3.3075801	-1.7554381	0.1706703	0.0353180	-0.0915837	-0.0520288	-3.1684987	2.1891348	-1.1028887	-0.2416110	7.2081800	-0.3004423	-0.9107321	-4.4973391	-0.5564927	0.5444993	-1.5361490	-0.7093641	0.6470038	0.5083350	0.4722171	0.8991640	-0.5335278	2.0677709	0.2908276	-0.2484117	0.5550592	-0.7849217	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-0.1191818	0.6758856	-1.2024273	-0.7813405	1.0737029	1.1149698	-7.7955680	-7.8028518	-7.7819186	0.9890100	1.2389155	1.1056816
0.7641795	-0.6224522	-2.1167121	0.1331322	-0.7743774	-1.4895254	-0.2577889	-1.3355179	1.9176356	-0.0790204	-0.2416110	-0.1655192	-1.3737277	1.0862459	-2.2358353	-0.6350417	1.0871605	-1.5361490	1.6982368	0.0295777	2.4495715	0.4722171	-0.8209490	2.0768430	-0.4631427	0.6912573	-0.4203333	0.6373022	-0.7849217	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	1.2152581	2.0244149	-1.2024273	-0.7813405	1.1448570	1.2555304	0.1953284	0.1420107	0.2150929	-0.8234122	-0.5069308	0.2980362
0.7189708	-1.2553927	-1.9680439	0.1130268	-1.0980928	-1.9361672	-0.6481228	-1.2301612	2.0452170	0.7748357	-0.2416110	-0.1655192	-1.8370737	1.7238573	-2.1058477	-0.3056405	0.9900693	-1.5361490	1.7601503	0.5781693	2.5123629	0.4722171	-0.2012539	1.7467179	2.0634648	0.8765288	0.6177527	0.4326386	-0.7849217	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	0.5250170	2.5731715	-1.2024273	-0.7813405	1.0737029	1.3006052	0.2007598	0.1372865	0.2061025	-1.5638648	-1.2876722	0.0912259
0.7242923	-1.2989464	-1.8694781	0.0481745	0.1178533	-1.1097980	-1.6020540	0.3913681	1.9100175	-1.1028887	2.3795348	-0.1655192	-0.2980879	-0.9107321	-0.1000316	0.1250748	1.0517878	-1.5361490	1.5828152	0.4925709	2.2800137	0.4722171	-0.1519738	1.7904106	2.1522253	0.6452677	-0.2701538	0.4755646	-0.7849217	-0.1128779	1.0855736	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-0.4319047	2.9608505	-1.2024273	-0.7813405	-0.9072150	-0.9131378	0.1996343	0.1124953	0.1858714	-1.8634065	-1.6346765	0.2155543
0.9352516	-1.3793536	-3.0269529	0.0215361	0.0900540	0.1332152	-0.1066436	-0.1414825	2.0377199	-0.8662133	-0.2416110	-0.1655192	-0.3692318	-0.3089347	-0.6620418	0.0206950	0.7681656	-1.5361490	1.8300773	0.6846485	2.9304573	0.4722171	0.2054028	1.9100254	2.1582016	0.7810711	-0.1544723	0.4325190	-0.7849217	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	0.2868788	3.2255853	-1.2024273	-0.7813405	1.2451515	1.2447437	0.1914616	0.1272668	0.2209386	-2.2095334	-2.0670853	0.1783289
0.8444331	-0.9330949	-2.9443530	0.0747295	-0.7695606	-0.9565209	-0.3344822	-0.6036707	1.8805892	0.1310209	-0.2416110	-0.1655192	-1.5238491	1.1997774	-1.3328933	-0.3090592	0.9778643	-1.5361490	1.8112041	0.0716776	2.5471763	0.4722171	-0.6926950	1.7248578	2.1822881	0.5215356	-0.4246885	0.5017085	-0.7849217	-0.1128779	0.6772291	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-0.2706541	3.1618692	-1.2024273	-0.7813405	-0.9072150	-0.9131378	0.1948107	0.1064054	0.2122564	-3.3992545	-3.2647966	0.3128996
-0.7153664	0.4502275	1.0481024	-0.0805202	-0.4000201	-0.9808023	-1.0769526	-0.2862954	0.2005249	0.8699766	-0.2416110	-0.1655192	-0.8646722	1.0463117	0.1751368	-0.0594924	-0.0348250	0.8218737	-0.7093641	-0.4416738	-0.2159140	0.4605887	-0.0186274	1.9011654	-0.4631427	-0.0177133	-0.4902254	0.7010200	-0.7849217	-0.1128779	0.5193370	-0.2161285	-0.3002999	-0.1390876	3.7341486	-0.3663205	-0.0567962	-2.0024503	1.1270342	0.9143624	-0.7813405	-0.9072150	-0.9131378	0.1573051	0.1341345	0.0544739	-1.3245569	-1.4023724	0.8187568
-0.5617197	-1.1270253	1.0423437	-0.0866456	0.1640141	-1.0020259	-0.4873752	-1.4301914	1.6399948	-1.1028887	-0.2416110	-0.1655192	-0.0591290	-0.9107321	0.1704439	-0.3722444	0.2216118	0.3719354	-0.7093641	-0.6805169	1.0168585	0.4722171	0.6459055	1.8146778	2.2398990	0.2306910	-0.3986840	0.5758925	1.2739612	-0.1128779	0.7696186	-0.2161285	-0.3002999	-0.1390876	3.3975921	-0.3663205	-0.0567962	-0.9894272	1.8693170	1.1994568	-0.7813405	-0.9072150	-0.9131378	0.1768587	0.1536592	0.0416061	-0.7557411	-0.6951816	0.8100547
-1.2082406	-1.2306736	1.0501724	-0.3414420	0.4114874	-0.0459608	-1.3977370	-0.4182376	1.4924198	-1.1028887	-0.2416110	-0.1655192	0.1295388	-0.9107321	0.2830407	-0.2881221	0.3509980	0.1653352	-0.7093641	-0.6501137	0.6138227	0.4689071	0.4828230	1.9898128	2.0124254	0.5441359	-0.2635801	0.5653819	1.2025710	-0.1128779	0.5193370	-0.2161285	-0.3002999	-0.1390876	3.3975921	-0.3663205	-0.0567962	-1.7081830	1.8935895	-1.2024273	-0.7813405	-0.9072150	-0.9131378	0.1800239	0.1580294	0.0371551	-1.8954263	-1.7042597	0.8621822
-1.2218157	-2.1458777	1.0472711	-0.4187440	0.2164229	-0.0660772	-1.6659814	-0.7823979	1.7784410	-1.1028887	-0.2416110	-0.1655192	-0.1385491	-0.9107321	0.1004149	-0.0712315	-1.8559490	-0.2305276	-0.7093641	-0.6511766	0.8861615	0.4612104	1.4189413	1.8007144	2.1102863	0.2596872	-0.2988330	0.5505589	1.1019643	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	4.0707657	-0.3663205	-0.0567962	-0.6042839	1.4513650	-1.2024273	-0.7813405	-0.9072150	-0.9131378	0.1820769	0.1416890	0.0360817	-0.8128519	-0.5952688	1.0928640
-1.3708028	-0.8472663	-0.1926501	0.4392459	-0.8000716	0.1732351	1.0232963	-0.0980002	1.6102044	-0.3050653	-0.2416110	-0.1655192	-1.6511890	1.3478997	0.0241304	0.5400138	0.8896999	-0.4496998	-0.7093641	0.4328218	-0.9187399	0.4722171	0.8732309	1.6078827	2.0220934	0.4204362	-0.4902254	0.6322432	-0.7849217	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-2.0024503	0.3060351	-1.2024273	-0.7813405	-0.9072150	-0.9131378	0.1890920	0.1598796	0.2162693	-2.1040048	-1.7680941	-0.1275653
-0.8522738	0.7628507	-0.3887801	0.4533951	-1.1483852	0.3979112	0.8408895	-0.6615732	0.0462667	0.7735091	-0.2416110	-0.1655192	-0.6348772	-0.9107321	-0.1275297	0.6154390	-0.4640421	1.0087909	-0.7093641	0.8664643	-1.9146573	0.0456755	1.4897880	-0.5335278	-0.4631427	-1.3498798	0.0545749	-1.4290972	-0.7849217	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-2.0024503	-0.8573343	-1.2024273	-0.7813405	-0.9072150	-0.9131378	0.1326908	0.2640898	0.2559705	0.5623707	0.9042770	-0.0329944
-0.8941916	-1.6612829	-0.2745011	0.4293331	-0.4606625	-1.0769090	1.0552532	-0.0225813	2.0591483	-1.1028887	-0.2416110	-0.1655192	-1.0144047	-0.9107321	-0.4205530	-0.0047809	0.8834583	-1.5361490	-0.7093641	0.6382788	0.1164273	0.4675777	1.8028429	1.7637571	2.1385769	-0.2615317	-0.3268318	0.4430654	-0.7849217	-0.1128779	0.6772291	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-0.9894272	0.8174868	-1.2024273	-0.7813405	-0.9072150	-0.9131378	0.1886108	0.1743173	0.2339778	-1.8691041	-1.4944695	0.3226523
-0.9025533	-1.6225502	-0.2231239	0.4240828	-1.2092209	-0.3017642	1.0880789	-3.1684987	1.8622718	-0.1751019	-0.2416110	-0.1655192	-2.1667970	1.1801078	-2.0466775	0.5469642	0.9632107	-1.5361490	-0.7093641	0.3444656	0.4767794	0.4722171	-2.0289867	1.8660741	2.1791259	0.2694600	-0.3603655	0.5104978	-0.7849217	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-0.6042839	0.9731492	-1.2024273	-0.7813405	-0.9072150	-0.9131378	0.1906266	0.1383557	0.2280761	-2.1652121	-1.5199192	-0.3522967
-0.7212197	0.9578551	-0.5150556	0.4420828	-1.5211638	0.5167801	0.9272074	-1.6359655	0.4942077	1.3319873	-0.2416110	-0.1655192	-1.4518673	1.0570459	0.0761848	0.4923641	-0.8001192	1.0620990	-0.7093641	0.9936102	-1.5500890	0.3569701	-0.3117378	-0.5335278	-0.4631427	-0.6985375	-0.4902254	-1.4290972	-0.7849217	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-2.0024503	-0.4314683	-1.2024273	-0.7813405	-0.9072150	-0.9131378	0.0936797	0.3186799	0.2600218	-0.9413963	-0.5217222	0.4892643
-0.6126005	-0.7077031	-0.3145347	0.4183489	-1.7711304	-1.6476595	0.9927371	-3.1684987	1.6964022	0.6937097	-0.2416110	-0.1655192	-2.1648864	1.6494836	-0.2975385	0.4606745	0.4802486	0.6670032	1.4422589	0.5358234	-0.3314381	0.4659292	1.1190239	1.6706287	2.0881802	0.1266613	-0.4902254	0.5313346	-0.7849217	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-0.9894272	0.2943173	-1.2024273	-0.7813405	-0.9072150	-0.9131378	0.1821135	0.2227467	0.2307131	-1.4768446	-1.0125985	-0.3674272
-0.3242173	0.3496063	-0.3357717	0.4010168	-1.5381402	-0.7297678	0.8567485	-0.0082585	1.3178164	0.9872085	-0.2416110	-0.1655192	-1.3303268	0.3103970	-0.1873932	0.2963027	0.6375892	0.7910801	-0.7093641	0.6048476	0.1150764	0.4722171	2.3415351	1.8274305	2.0235190	0.7159974	-0.4902254	0.6013136	-0.7849217	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-1.4449486	1.1296676	-1.2024273	-0.7813405	-0.9072150	-0.9131378	0.1720495	0.2868188	0.2388820	-1.3491480	-1.0770065	-0.3061399
-0.1229755	-0.3740460	-0.3020525	0.3782214	-0.1970433	-1.3713362	0.7333711	0.4828768	0.8006936	-1.0153661	-0.2416110	-0.1655192	-0.6990035	0.9082337	0.3400542	0.4715302	0.8454156	0.3592098	-0.7093641	0.6201360	-0.7636133	0.4300341	-0.9435994	-0.5335278	-0.4631427	-0.3885831	-0.2086361	-1.4290972	0.9300293	-0.1128779	0.7696186	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-0.6042839	-0.4758021	0.9193252	-0.7813405	-0.9072150	-0.9131378	0.1863388	0.1838340	0.2328716	0.4775876	0.8545113	0.1287156
-0.6691769	0.8445447	-0.6034381	0.4194282	-2.1503066	0.6212286	0.7294676	-1.3134608	-0.2242970	1.4478214	-0.2416110	-0.1655192	-1.8675572	1.2242620	-0.1119268	0.3683664	-0.9556598	1.0824987	-0.7093641	1.0408001	-1.3410404	-0.2346174	0.6280498	-0.5335278	-0.4631427	-0.7795828	-0.4902254	0.5324644	-0.7849217	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-1.4449486	-0.5712797	0.8018620	-0.7813405	-0.9072150	-0.9131378	0.0783115	0.2950352	0.2621456	-0.3150179	0.0208781	0.6754504

No missing data is found. Handle missing values if any, possibly through imputation

2.3 Identify multi-collinear variables

Compute the correlation matrix and identify highly correlated variables:

Code

#df_pre_pca_abb <- df_pre_pca
# Abbreviate column names using R's built-in abbreviate function
#abbrev_colnames <- abbreviate(colnames(df_pre_pca_abb))

# Assign the abbreviated names back to the dataframe
#colnames(df_pre_pca_abb) <- abbrev_colnames

# Recalculate and plot the correlation matrix
cor_matrix <- cor(df_pre_pca) |> round(digits = 2)

# Convert the matrix to a data frame
cor_matrix_df <- as.data.frame(cor_matrix)

# Add row names as a new column
cor_matrix_df$Predictors <- rownames(cor_matrix)

# Move the 'RowNames' column to the first position
cor_matrix_df <- cor_matrix_df|> select(Predictors, everything())



# Create the gt table
cor_matrix_df|>
  gt()|>
  data_color(
    columns = -Predictors,  # Exclude the 'RowNames' column from colorization
    colors = scales::col_numeric(
      palette = c("darkred", "white", "darkblue"),
      domain = c(-1, 1)
    )
  ) |> tab_options(container.overflow.x = TRUE, container.overflow.y = TRUE)

Warning: Since gt v0.9.0, the `colors` argument has been deprecated.
• Please use the `fn` argument instead.
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Predictors	distance_to_plantation	distance_to_road	distance_to_commodity_processing_factory	distance_to_plantation_concession	distance_to_forest	distance_to_river	distance_to_burned_area	percentage_of_agricultural_area_small_holder_in_the_village	percentage_of_plantation_area_per_sub_district	percentage_of_forested_area_in_the_sub_district	percentage_of_shrubland_in_the_sub_district	percentage_of_water_area_compared_to_sub_district_area	distance_to_deforestation	percentage_deforestation_area_size	arable_land_percent	erosion_risk_t_ha_1_yr_1	indeks_bahaya_banjir	indeks_bahaya_longsor	buffer_to_500m_irigated_land	aridity_index	total_kk_berdasarkan_pengguna_dan_non_pengguna_listrik	rasio_elektrifikasi	rasio_sekolah_tinggi_sma_sederajat	rasio_pt	rasio_rs	rasio_faskes_1	rasio_pasar	rasio_minimarket_swalayan	banyak_kejadian_tanah_longsor_2018_2019	korban_jiwa_tanah_longsor_2018_2019	banyak_kejadian_banjir_2018_2019	korban_jiwa_banjir_2018_2019	banyak_kejadian_banjir_bandang_2018_2019	korban_jiwa_banjir_bandang_2018_2019	banyak_kejadian_kebakaran_hutan_dan_lahan_2018_2019	banyak_kejadian_kekeringan_lahan_2018_2019	korban_jiwa_kekeringan_lahan_2018_2019	jumlah_sistem_peringatan_dini_bencana_alam	persentase_sistem_peringatan_dini_bencana_alam	rasio_embung_di_kecamatan	rasio_pasar_desa_pasar_hewan_pelelangan_ikan_pelelangan_hasil_pertanian_dll	jumlah_warga_penderita_gizi_buruk_marasmus_dan_kwashiorkor_pada_tahun_2018	rasio_warga_penderita_gizi_buruk_marasmus_dan_kwashiorkor_pada_tahun_2018	annual_mean_temp	temp_change	annual_mean_prec	rasio_40pers_ekon_rendah_rt	rasio_40pers_ekon_rendah_indv	prec_change
distance_to_plantation	1.00	0.05	0.16	-0.42	-0.01	0.32	0.03	-0.21	-0.04	0.01	0.08	0.08	0.04	0.03	-0.18	-0.26	-0.13	-0.11	-0.16	-0.30	0.00	-0.04	0.07	0.03	0.01	-0.06	0.15	-0.19	-0.07	0.07	-0.03	0.03	0.10	0.13	-0.07	-0.03	-0.02	-0.11	0.07	0.09	-0.11	0.10	0.09	-0.11	-0.13	-0.14	0.13	0.09	0.07
distance_to_road	0.05	1.00	0.21	-0.01	-0.48	0.29	0.17	-0.10	-0.58	0.68	0.07	-0.13	-0.33	0.56	0.09	-0.05	-0.41	0.49	-0.20	0.09	-0.45	-0.29	-0.10	-0.34	-0.37	-0.22	0.16	-0.32	0.25	0.02	-0.03	-0.04	-0.06	-0.03	0.07	0.09	0.00	-0.05	-0.50	0.08	0.09	0.03	0.01	-0.05	0.00	0.00	0.32	0.28	0.13
distance_to_commodity_processing_factory	0.16	0.21	1.00	-0.30	0.15	0.37	0.23	0.11	-0.21	0.03	0.16	-0.16	0.19	0.03	0.28	-0.23	-0.01	-0.06	-0.17	-0.63	0.00	-0.03	-0.12	-0.16	-0.17	-0.06	0.15	0.00	-0.10	-0.01	0.08	-0.01	-0.03	-0.01	0.12	0.09	-0.09	0.14	-0.09	0.33	0.21	0.00	0.01	0.05	0.01	-0.05	0.06	-0.06	-0.46
distance_to_plantation_concession	-0.42	-0.01	-0.30	1.00	-0.06	-0.55	-0.46	0.15	0.04	0.03	0.07	-0.01	-0.04	-0.01	-0.08	0.21	0.02	0.05	0.06	0.62	0.02	-0.05	0.01	0.06	0.02	0.06	-0.26	0.11	0.07	-0.04	0.02	-0.03	-0.13	-0.15	0.04	0.01	0.03	0.09	-0.04	0.03	0.00	0.03	0.02	-0.06	0.00	0.02	-0.06	0.01	0.08
distance_to_forest	-0.01	-0.48	0.15	-0.06	1.00	-0.05	-0.05	0.37	0.30	-0.79	0.19	0.05	0.89	-0.72	0.25	-0.24	0.31	-0.51	0.20	-0.45	0.34	0.29	-0.09	0.04	0.02	0.23	-0.06	0.21	-0.31	-0.07	0.03	0.04	0.02	-0.05	-0.03	-0.03	-0.02	0.25	0.23	0.00	0.07	-0.01	0.02	-0.04	-0.09	-0.13	-0.11	-0.15	-0.19
distance_to_river	0.32	0.29	0.37	-0.55	-0.05	1.00	0.41	-0.25	-0.24	0.16	0.00	0.02	0.01	0.14	-0.06	-0.24	-0.40	0.15	-0.33	-0.36	-0.22	-0.11	-0.04	-0.27	-0.22	-0.21	0.18	-0.30	0.05	0.05	-0.24	-0.13	-0.11	-0.07	0.05	-0.02	0.01	-0.11	-0.18	0.07	0.04	-0.03	-0.02	-0.17	-0.19	-0.20	0.17	0.10	-0.11
distance_to_burned_area	0.03	0.17	0.23	-0.46	-0.05	0.41	1.00	-0.20	-0.01	0.09	-0.04	-0.02	-0.10	0.21	-0.02	-0.11	-0.04	0.00	-0.17	-0.27	-0.17	-0.03	0.01	-0.10	-0.03	-0.14	0.20	-0.15	-0.04	-0.11	-0.11	-0.11	-0.16	-0.04	-0.02	-0.03	0.01	-0.01	-0.20	-0.19	0.12	0.03	0.02	-0.08	-0.10	-0.10	-0.01	-0.03	-0.20
percentage_of_agricultural_area_small_holder_in_the_village	-0.21	-0.10	0.11	0.15	0.37	-0.25	-0.20	1.00	-0.15	-0.22	0.07	-0.09	0.36	-0.26	0.78	0.23	0.28	-0.05	0.25	-0.04	0.14	0.11	-0.16	-0.09	-0.15	0.12	-0.13	0.21	-0.01	-0.01	0.22	0.12	0.12	0.05	-0.04	0.09	0.03	0.15	0.06	0.22	0.19	-0.04	-0.02	0.39	0.38	0.36	0.05	0.01	-0.20
percentage_of_plantation_area_per_sub_district	-0.04	-0.58	-0.21	0.04	0.30	-0.24	-0.01	-0.15	1.00	-0.40	0.04	0.09	0.20	-0.25	-0.30	-0.20	0.47	-0.57	0.35	-0.16	0.59	0.28	0.16	0.48	0.47	0.29	-0.18	0.38	-0.34	-0.02	0.10	-0.02	0.04	0.03	0.00	-0.03	0.04	0.05	0.66	-0.32	-0.13	0.02	0.02	-0.14	-0.18	-0.19	-0.51	-0.47	0.04
percentage_of_forested_area_in_the_sub_district	0.01	0.68	0.03	0.03	-0.79	0.16	0.09	-0.22	-0.40	1.00	-0.10	-0.09	-0.74	0.81	-0.07	0.17	-0.34	0.56	-0.17	0.33	-0.30	-0.34	-0.02	-0.21	-0.22	-0.24	0.13	-0.19	0.30	0.10	0.00	-0.05	-0.01	0.02	0.12	0.14	0.04	-0.07	-0.30	0.09	0.04	0.06	0.05	0.03	0.06	0.10	0.28	0.26	0.08
percentage_of_shrubland_in_the_sub_district	0.08	0.07	0.16	0.07	0.19	0.00	-0.04	0.07	0.04	-0.10	1.00	0.01	0.21	-0.03	0.01	-0.13	0.17	-0.23	0.05	-0.15	0.12	0.02	-0.08	0.01	0.03	0.04	-0.01	0.11	-0.16	-0.03	0.18	-0.05	-0.07	-0.03	0.04	0.02	-0.01	0.12	0.06	0.05	0.13	0.01	0.02	0.04	0.03	0.01	-0.19	-0.20	-0.08
percentage_of_water_area_compared_to_sub_district_area	0.08	-0.13	-0.16	-0.01	0.05	0.02	-0.02	-0.09	0.09	-0.09	0.01	1.00	0.01	-0.06	-0.17	-0.02	0.07	-0.06	0.04	0.07	0.08	0.06	0.13	0.01	0.23	0.07	-0.02	0.03	-0.07	-0.02	0.02	-0.04	-0.05	-0.02	-0.01	-0.03	-0.01	-0.04	0.12	-0.07	-0.06	0.06	0.05	-0.19	-0.19	-0.18	-0.12	-0.09	0.07
distance_to_deforestation	0.04	-0.33	0.19	-0.04	0.89	0.01	-0.10	0.36	0.20	-0.74	0.21	0.01	1.00	-0.79	0.22	-0.27	0.21	-0.42	0.14	-0.46	0.22	0.24	-0.12	-0.03	-0.05	0.19	-0.09	0.10	-0.27	-0.10	0.02	0.02	0.04	-0.07	-0.03	-0.04	0.02	0.20	0.12	0.02	0.06	-0.07	-0.05	-0.06	-0.10	-0.15	-0.03	-0.07	-0.06
percentage_deforestation_area_size	0.03	0.56	0.03	-0.01	-0.72	0.14	0.21	-0.26	-0.25	0.81	-0.03	-0.06	-0.79	1.00	-0.13	0.09	-0.23	0.34	-0.09	0.26	-0.21	-0.26	0.04	-0.12	-0.11	-0.20	0.13	-0.15	0.21	0.09	0.04	-0.01	-0.06	0.03	0.14	0.09	-0.05	-0.06	-0.21	0.01	0.06	0.10	0.08	-0.01	0.01	0.04	0.12	0.13	0.04
arable_land_percent	-0.18	0.09	0.28	-0.08	0.25	-0.06	-0.02	0.78	-0.30	-0.07	0.01	-0.17	0.22	-0.13	1.00	0.37	0.06	0.20	0.10	-0.09	-0.04	0.05	-0.17	-0.22	-0.26	0.06	0.03	0.07	0.07	0.03	0.12	0.07	0.10	0.03	0.04	0.04	0.01	0.06	-0.09	0.25	0.23	-0.08	-0.08	0.54	0.53	0.51	0.17	0.11	-0.27
erosion_risk_t_ha_1_yr_1	-0.26	-0.05	-0.23	0.21	-0.24	-0.24	-0.11	0.23	-0.20	0.17	-0.13	-0.02	-0.27	0.09	0.37	1.00	-0.12	0.46	-0.10	0.54	-0.15	-0.14	-0.05	-0.07	-0.04	-0.06	-0.04	0.00	0.31	0.05	-0.06	-0.09	0.03	-0.04	0.05	0.05	0.02	-0.03	-0.16	0.10	0.06	-0.05	-0.06	0.57	0.60	0.63	0.09	0.12	0.08
indeks_bahaya_banjir	-0.13	-0.41	-0.01	0.02	0.31	-0.40	-0.04	0.28	0.47	-0.34	0.17	0.07	0.21	-0.23	0.06	-0.12	1.00	-0.63	0.56	-0.23	0.55	0.30	0.00	0.32	0.27	0.33	-0.07	0.56	-0.41	-0.11	0.49	0.18	0.06	0.04	-0.06	0.04	-0.06	0.21	0.50	-0.15	0.07	0.11	0.13	0.23	0.16	0.14	-0.44	-0.44	-0.22
indeks_bahaya_longsor	-0.11	0.49	-0.06	0.05	-0.51	0.15	0.00	-0.05	-0.57	0.56	-0.23	-0.06	-0.42	0.34	0.20	0.46	-0.63	1.00	-0.48	0.43	-0.49	-0.25	0.00	-0.34	-0.30	-0.22	0.08	-0.31	0.50	0.10	-0.17	-0.13	-0.04	-0.03	0.06	0.06	0.05	-0.15	-0.47	0.27	0.00	-0.06	-0.07	0.12	0.18	0.22	0.37	0.37	0.13
buffer_to_500m_irigated_land	-0.16	-0.20	-0.17	0.06	0.20	-0.33	-0.17	0.25	0.35	-0.17	0.05	0.04	0.14	-0.09	0.10	-0.10	0.56	-0.48	1.00	-0.08	0.37	0.18	-0.07	0.18	0.12	0.21	-0.08	0.31	-0.32	-0.06	0.22	0.09	0.16	0.00	-0.01	0.10	-0.04	0.11	0.36	-0.23	0.12	0.09	0.08	0.12	0.09	0.07	-0.24	-0.22	0.07
aridity_index	-0.30	0.09	-0.63	0.62	-0.45	-0.36	-0.27	-0.04	-0.16	0.33	-0.15	0.07	-0.46	0.26	-0.09	0.54	-0.23	0.43	-0.08	1.00	-0.22	-0.17	0.07	-0.02	0.02	-0.07	-0.13	-0.10	0.32	0.05	-0.08	-0.04	-0.15	-0.12	0.01	-0.04	0.06	-0.08	-0.21	-0.07	-0.06	0.08	0.06	0.11	0.19	0.27	0.06	0.15	0.27
total_kk_berdasarkan_pengguna_dan_non_pengguna_listrik	0.00	-0.45	0.00	0.02	0.34	-0.22	-0.17	0.14	0.59	-0.30	0.12	0.08	0.22	-0.21	-0.04	-0.15	0.55	-0.49	0.37	-0.22	1.00	0.26	0.02	0.44	0.44	0.41	-0.12	0.58	-0.23	0.00	0.30	0.09	0.12	0.07	0.08	0.04	-0.12	0.52	0.81	0.02	0.07	0.13	0.16	0.11	0.05	0.04	-0.50	-0.53	-0.32
rasio_elektrifikasi	-0.04	-0.29	-0.03	-0.05	0.29	-0.11	-0.03	0.11	0.28	-0.34	0.02	0.06	0.24	-0.26	0.05	-0.14	0.30	-0.25	0.18	-0.17	0.26	1.00	0.14	0.20	0.19	0.22	-0.02	0.30	-0.16	0.02	0.05	0.05	0.11	0.06	0.06	0.01	0.03	0.00	0.30	-0.09	-0.05	0.01	0.03	0.00	-0.04	-0.05	-0.32	-0.32	-0.05
rasio_sekolah_tinggi_sma_sederajat	0.07	-0.10	-0.12	0.01	-0.09	-0.04	0.01	-0.16	0.16	-0.02	-0.08	0.13	-0.12	0.04	-0.17	-0.05	0.00	0.00	-0.07	0.07	0.02	0.14	1.00	0.29	0.31	0.00	-0.05	0.06	0.06	0.12	0.04	0.01	0.03	0.14	0.09	-0.05	-0.12	-0.07	0.07	0.02	-0.13	-0.01	-0.01	-0.10	-0.10	-0.08	-0.20	-0.17	0.00
rasio_pt	0.03	-0.34	-0.16	0.06	0.04	-0.27	-0.10	-0.09	0.48	-0.21	0.01	0.01	-0.03	-0.12	-0.22	-0.07	0.32	-0.34	0.18	-0.02	0.44	0.20	0.29	1.00	0.65	0.23	-0.10	0.33	-0.11	0.00	0.10	0.03	-0.02	0.05	0.08	0.03	-0.03	0.05	0.48	-0.16	-0.13	0.03	0.05	0.08	0.06	0.07	-0.58	-0.53	-0.02
rasio_rs	0.01	-0.37	-0.17	0.02	0.02	-0.22	-0.03	-0.15	0.47	-0.22	0.03	0.23	-0.05	-0.11	-0.26	-0.04	0.27	-0.30	0.12	0.02	0.44	0.19	0.31	0.65	1.00	0.19	-0.10	0.25	-0.10	-0.05	0.05	-0.06	-0.01	0.01	0.05	0.00	-0.03	0.05	0.48	-0.21	-0.18	-0.05	-0.03	0.00	-0.02	-0.01	-0.63	-0.58	0.03
rasio_faskes_1	-0.06	-0.22	-0.06	0.06	0.23	-0.21	-0.14	0.12	0.29	-0.24	0.04	0.07	0.19	-0.20	0.06	-0.06	0.33	-0.22	0.21	-0.07	0.41	0.22	0.00	0.23	0.19	1.00	-0.09	0.25	-0.17	-0.05	0.19	0.12	0.06	0.06	0.01	0.06	-0.02	0.14	0.39	-0.01	0.01	0.09	0.10	0.09	0.07	0.06	-0.26	-0.27	-0.12
rasio_pasar	0.15	0.16	0.15	-0.26	-0.06	0.18	0.20	-0.13	-0.18	0.13	-0.01	-0.02	-0.09	0.13	0.03	-0.04	-0.07	0.08	-0.08	-0.13	-0.12	-0.02	-0.05	-0.10	-0.10	-0.09	1.00	-0.14	0.01	0.00	-0.07	-0.01	-0.03	-0.02	-0.03	-0.02	-0.03	0.02	-0.15	-0.03	0.13	-0.03	-0.04	0.05	0.04	0.04	0.06	0.00	-0.05
rasio_minimarket_swalayan	-0.19	-0.32	0.00	0.11	0.21	-0.30	-0.15	0.21	0.38	-0.19	0.11	0.03	0.10	-0.15	0.07	0.00	0.56	-0.31	0.31	-0.10	0.58	0.30	0.06	0.33	0.25	0.25	-0.14	1.00	-0.16	-0.11	0.37	0.12	0.07	0.05	0.08	0.02	-0.08	0.33	0.45	0.03	0.07	0.16	0.18	0.15	0.11	0.10	-0.41	-0.42	-0.21
banyak_kejadian_tanah_longsor_2018_2019	-0.07	0.25	-0.10	0.07	-0.31	0.05	-0.04	-0.01	-0.34	0.30	-0.16	-0.07	-0.27	0.21	0.07	0.31	-0.41	0.50	-0.32	0.32	-0.23	-0.16	0.06	-0.11	-0.10	-0.17	0.01	-0.16	1.00	0.17	-0.05	-0.12	0.02	0.02	0.21	0.15	0.06	-0.02	-0.25	0.17	0.03	0.00	-0.01	0.04	0.09	0.12	0.22	0.21	0.13
korban_jiwa_tanah_longsor_2018_2019	0.07	0.02	-0.01	-0.04	-0.07	0.05	-0.11	-0.01	-0.02	0.10	-0.03	-0.02	-0.10	0.09	0.03	0.05	-0.11	0.10	-0.06	0.05	0.00	0.02	0.12	0.00	-0.05	-0.05	0.00	-0.11	0.17	1.00	-0.02	-0.02	0.19	0.20	0.06	-0.04	-0.01	-0.09	0.06	0.07	0.03	-0.02	-0.05	0.01	0.00	0.01	0.06	0.03	-0.04
banyak_kejadian_banjir_2018_2019	-0.03	-0.03	0.08	0.02	0.03	-0.24	-0.11	0.22	0.10	0.00	0.18	0.02	0.02	0.04	0.12	-0.06	0.49	-0.17	0.22	-0.08	0.30	0.05	0.04	0.10	0.05	0.19	-0.07	0.37	-0.05	-0.02	1.00	0.23	0.09	0.04	0.03	0.15	-0.06	0.18	0.23	0.14	0.18	0.17	0.17	0.15	0.12	0.11	-0.14	-0.17	-0.19
korban_jiwa_banjir_2018_2019	0.03	-0.04	-0.01	-0.03	0.04	-0.13	-0.11	0.12	-0.02	-0.05	-0.05	-0.04	0.02	-0.01	0.07	-0.09	0.18	-0.13	0.09	-0.04	0.09	0.05	0.01	0.03	-0.06	0.12	-0.01	0.12	-0.12	-0.02	0.23	1.00	0.14	0.17	-0.02	0.02	-0.01	0.05	0.07	0.05	-0.04	0.15	0.13	0.04	0.02	0.02	0.02	0.01	-0.12
banyak_kejadian_banjir_bandang_2018_2019	0.10	-0.06	-0.03	-0.13	0.02	-0.11	-0.16	0.12	0.04	-0.01	-0.07	-0.05	0.04	-0.06	0.10	0.03	0.06	-0.04	0.16	-0.15	0.12	0.11	0.03	-0.02	-0.01	0.06	-0.03	0.07	0.02	0.19	0.09	0.14	1.00	0.46	0.04	0.08	-0.02	-0.04	0.17	0.12	0.06	0.01	0.03	0.05	0.02	0.02	0.07	0.04	0.09
korban_jiwa_banjir_bandang_2018_2019	0.13	-0.03	-0.01	-0.15	-0.05	-0.07	-0.04	0.05	0.03	0.02	-0.03	-0.02	-0.07	0.03	0.03	-0.04	0.04	-0.03	0.00	-0.12	0.07	0.06	0.14	0.05	0.01	0.06	-0.02	0.05	0.02	0.20	0.04	0.17	0.46	1.00	-0.04	0.10	-0.01	-0.06	0.13	0.12	-0.02	0.01	-0.01	0.02	0.01	0.00	0.04	0.03	0.01
banyak_kejadian_kebakaran_hutan_dan_lahan_2018_2019	-0.07	0.07	0.12	0.04	-0.03	0.05	-0.02	-0.04	0.00	0.12	0.04	-0.01	-0.03	0.14	0.04	0.05	-0.06	0.06	-0.01	0.01	0.08	0.06	0.09	0.08	0.05	0.01	-0.03	0.08	0.21	0.06	0.03	-0.02	0.04	-0.04	1.00	0.16	-0.02	0.01	0.09	0.03	0.08	0.00	-0.02	0.03	0.03	0.03	-0.07	-0.07	0.02
banyak_kejadian_kekeringan_lahan_2018_2019	-0.03	0.09	0.09	0.01	-0.03	-0.02	-0.03	0.09	-0.03	0.14	0.02	-0.03	-0.04	0.09	0.04	0.05	0.04	0.06	0.10	-0.04	0.04	0.01	-0.05	0.03	0.00	0.06	-0.02	0.02	0.15	-0.04	0.15	0.02	0.08	0.10	0.16	1.00	0.18	0.03	0.03	0.15	0.02	0.04	0.05	0.04	0.04	0.03	0.03	0.01	0.01
korban_jiwa_kekeringan_lahan_2018_2019	-0.02	0.00	-0.09	0.03	-0.02	0.01	0.01	0.03	0.04	0.04	-0.01	-0.01	0.02	-0.05	0.01	0.02	-0.06	0.05	-0.04	0.06	-0.12	0.03	-0.12	-0.03	-0.03	-0.02	-0.03	-0.08	0.06	-0.01	-0.06	-0.01	-0.02	-0.01	-0.02	0.18	1.00	-0.12	-0.06	-0.07	-0.04	-0.05	-0.05	0.00	0.02	0.01	0.02	0.03	0.10
jumlah_sistem_peringatan_dini_bencana_alam	-0.11	-0.05	0.14	0.09	0.25	-0.11	-0.01	0.15	0.05	-0.07	0.12	-0.04	0.20	-0.06	0.06	-0.03	0.21	-0.15	0.11	-0.08	0.52	0.00	-0.07	0.05	0.05	0.14	0.02	0.33	-0.02	-0.09	0.18	0.05	-0.04	-0.06	0.01	0.03	-0.12	1.00	-0.07	0.21	0.24	0.16	0.19	0.10	0.08	0.06	0.03	-0.01	-0.30
persentase_sistem_peringatan_dini_bencana_alam	0.07	-0.50	-0.09	-0.04	0.23	-0.18	-0.20	0.06	0.66	-0.30	0.06	0.12	0.12	-0.21	-0.09	-0.16	0.50	-0.47	0.36	-0.21	0.81	0.30	0.07	0.48	0.48	0.39	-0.15	0.45	-0.25	0.06	0.23	0.07	0.17	0.13	0.09	0.03	-0.06	-0.07	1.00	-0.12	-0.09	0.04	0.06	0.07	0.01	0.00	-0.60	-0.61	-0.17
rasio_embung_di_kecamatan	0.09	0.08	0.33	0.03	0.00	0.07	-0.19	0.22	-0.32	0.09	0.05	-0.07	0.02	0.01	0.25	0.10	-0.15	0.27	-0.23	-0.07	0.02	-0.09	0.02	-0.16	-0.21	-0.01	-0.03	0.03	0.17	0.07	0.14	0.05	0.12	0.12	0.03	0.15	-0.07	0.21	-0.12	1.00	0.16	0.08	0.09	0.08	0.07	0.06	0.25	0.18	-0.31
rasio_pasar_desa_pasar_hewan_pelelangan_ikan_pelelangan_hasil_pertanian_dll	-0.11	0.09	0.21	0.00	0.07	0.04	0.12	0.19	-0.13	0.04	0.13	-0.06	0.06	0.06	0.23	0.06	0.07	0.00	0.12	-0.06	0.07	-0.05	-0.13	-0.13	-0.18	0.01	0.13	0.07	0.03	0.03	0.18	-0.04	0.06	-0.02	0.08	0.02	-0.04	0.24	-0.09	0.16	1.00	0.05	0.05	0.10	0.08	0.08	0.08	0.01	-0.27
jumlah_warga_penderita_gizi_buruk_marasmus_dan_kwashiorkor_pada_tahun_2018	0.10	0.03	0.00	0.03	-0.01	-0.03	0.03	-0.04	0.02	0.06	0.01	0.06	-0.07	0.10	-0.08	-0.05	0.11	-0.06	0.09	0.08	0.13	0.01	-0.01	0.03	-0.05	0.09	-0.03	0.16	0.00	-0.02	0.17	0.15	0.01	0.01	0.00	0.04	-0.05	0.16	0.04	0.08	0.05	1.00	0.97	-0.07	-0.08	-0.07	0.02	0.00	-0.11
rasio_warga_penderita_gizi_buruk_marasmus_dan_kwashiorkor_pada_tahun_2018	0.09	0.01	0.01	0.02	0.02	-0.02	0.02	-0.02	0.02	0.05	0.02	0.05	-0.05	0.08	-0.08	-0.06	0.13	-0.07	0.08	0.06	0.16	0.03	-0.01	0.05	-0.03	0.10	-0.04	0.18	-0.01	-0.05	0.17	0.13	0.03	-0.01	-0.02	0.05	-0.05	0.19	0.06	0.09	0.05	0.97	1.00	-0.05	-0.06	-0.05	0.00	-0.02	-0.14
annual_mean_temp	-0.11	-0.05	0.05	-0.06	-0.04	-0.17	-0.08	0.39	-0.14	0.03	0.04	-0.19	-0.06	-0.01	0.54	0.57	0.23	0.12	0.12	0.11	0.11	0.00	-0.10	0.08	0.00	0.09	0.05	0.15	0.04	0.01	0.15	0.04	0.05	0.02	0.03	0.04	0.00	0.10	0.07	0.08	0.10	-0.07	-0.05	1.00	0.99	0.98	-0.13	-0.16	-0.17
temp_change	-0.13	0.00	0.01	0.00	-0.09	-0.19	-0.10	0.38	-0.18	0.06	0.03	-0.19	-0.10	0.01	0.53	0.60	0.16	0.18	0.09	0.19	0.05	-0.04	-0.10	0.06	-0.02	0.07	0.04	0.11	0.09	0.00	0.12	0.02	0.02	0.01	0.03	0.04	0.02	0.08	0.01	0.07	0.08	-0.08	-0.06	0.99	1.00	0.99	-0.10	-0.12	-0.12
annual_mean_prec	-0.14	0.00	-0.05	0.02	-0.13	-0.20	-0.10	0.36	-0.19	0.10	0.01	-0.18	-0.15	0.04	0.51	0.63	0.14	0.22	0.07	0.27	0.04	-0.05	-0.08	0.07	-0.01	0.06	0.04	0.10	0.12	0.01	0.11	0.02	0.02	0.00	0.03	0.03	0.01	0.06	0.00	0.06	0.08	-0.07	-0.05	0.98	0.99	1.00	-0.09	-0.10	-0.09
rasio_40pers_ekon_rendah_rt	0.13	0.32	0.06	-0.06	-0.11	0.17	-0.01	0.05	-0.51	0.28	-0.19	-0.12	-0.03	0.12	0.17	0.09	-0.44	0.37	-0.24	0.06	-0.50	-0.32	-0.20	-0.58	-0.63	-0.26	0.06	-0.41	0.22	0.06	-0.14	0.02	0.07	0.04	-0.07	0.03	0.02	0.03	-0.60	0.25	0.08	0.02	0.00	-0.13	-0.10	-0.09	1.00	0.98	0.10
rasio_40pers_ekon_rendah_indv	0.09	0.28	-0.06	0.01	-0.15	0.10	-0.03	0.01	-0.47	0.26	-0.20	-0.09	-0.07	0.13	0.11	0.12	-0.44	0.37	-0.22	0.15	-0.53	-0.32	-0.17	-0.53	-0.58	-0.27	0.00	-0.42	0.21	0.03	-0.17	0.01	0.04	0.03	-0.07	0.01	0.03	-0.01	-0.61	0.18	0.01	0.00	-0.02	-0.16	-0.12	-0.10	0.98	1.00	0.19
prec_change	0.07	0.13	-0.46	0.08	-0.19	-0.11	-0.20	-0.20	0.04	0.08	-0.08	0.07	-0.06	0.04	-0.27	0.08	-0.22	0.13	0.07	0.27	-0.32	-0.05	0.00	-0.02	0.03	-0.12	-0.05	-0.21	0.13	-0.04	-0.19	-0.12	0.09	0.01	0.02	0.01	0.10	-0.30	-0.17	-0.31	-0.27	-0.11	-0.14	-0.17	-0.12	-0.09	0.10	0.19	1.00

Code

# Set a threshold value for correlation
threshold <- 0.8

# Find the indices of the variables that are highly correlated according to the specified threshold in the correlation matrix 'cor_matrix.'
# This will be used to remove the highly correlated variables from 'df_pre_pca.'
highly_correlated <- findCorrelation(cor(df_pre_pca), cutoff = threshold, names = FALSE)

# If you also need the names of the highly correlated variables, you can extract them using the indices.
highly_correlated_names <- colnames(cor(df_pre_pca))[highly_correlated]


# # Remove the columns from 'df_pre_pca' that correspond to the indices of the highly correlated variables.
# df_pre_pca <- df_pre_pca |> dplyr::select(-highly_correlated_names[[1]])
# Create a data frame from highly_correlated_names and threshold
highly_correlated_df <- data.frame(
  Predictor = highly_correlated_names
 # Threshold = threshold
)

# Create a gt table
highly_correlated_df|>
  gt()|>
  tab_header(
    title = "Highly Correlated Predictors",
    subtitle = paste("Predictors with correlation above", threshold)
  )|>
  cols_label(
    Predictor = "Predictor Name"
   # Threshold = "Correlation Threshold"
  )

Highly Correlated Predictors
Predictors with correlation above 0.8
Predictor Name
total_kk_berdasarkan_pengguna_dan_non_pengguna_listrik
percentage_of_forested_area_in_the_sub_district
rasio_40pers_ekon_rendah_rt
distance_to_forest
annual_mean_temp
annual_mean_prec
jumlah_warga_penderita_gizi_buruk_marasmus_dan_kwashiorkor_pada_tahun_2018

3 Exploratory data analysis (EDA)

Visualize the data and examine any patterns, distributions, or outliers. In Principal Component Analysis (PCA), you want to reduce the dimensionality of your dataset to uncover patterns and make visualization easier. However, if some variables (columns) have constant or near-constant values across the observations, they can’t contribute to explaining the variability in your data. Such columns are advised to be removed before performing PCA.

Code

# Pivot the 'scaled_df_complete_temp' dataframe to long format
# Exclude certain columns from being pivoted and specify the new column names for 'variable' and 'value'
df_long <- scaled_df_complete_temp |> 
  dplyr::select(1:9) |> bind_cols(df_pre_pca) |> 
  tidyr::pivot_longer(
    cols = -c(idkec_dum, sumber, kdprov, nmprov, nmkab, nmkec, periode, kdkab, kdkec),
    names_to = "variable",
    values_to = "value"
  )

# Select only the 'variable' and 'value' columns from the long-form data
# Remove unwanted columns and group by 'variable' to prepare for summarization
gt_tab <- df_long |>
  dplyr::select(-c(idkec_dum, sumber, kdprov, nmprov, nmkab, nmkec, periode, kdkab, kdkec)) |>
  group_by(variable) 

# Calculate summary statistics for each group (each 'variable')
# Also, keep the original 'value' data in a list column called 'value_data'
# Use '.groups = "drop"' to return a regular dataframe rather than a grouped one
gt_stat <- gt_tab |> 
  summarise(
    min = min(value, na.rm = TRUE),
    max = max(value, na.rm = TRUE),
    median = median(value, na.rm = TRUE),
    #mean = mean(value, na.rm = TRUE),
    #sd = sd(value, na.rm = TRUE),
    value_data = list(value),
    .groups = "drop"
  )

# Create a GT table with a density plot column
# The density plot is generated from the 'value_data' list column
# Customize the appearance of the density plot and format the number columns
gt_stat |>
  gt::gt() |> 
  gtExtras::gt_plt_dist(
    value_data,
    type = "density",
    line_color = "blue",
    fill_color = "red"
  ) |> gt::fmt_number(columns = min:median, decimals = 1) |> 
  cols_label(
    variable = "Predictors",
    min = "Minimum",
    max = "Maximum",
    median = "Median",
    value_data = "Density"
  ) 

Predictors	Minimum	Maximum	Median	Density
annual_mean_prec	−7.8	0.3	0.1
annual_mean_temp	−7.8	0.2	0.2
arable_land_percent	−4.5	0.6	0.3
aridity_index	−4.3	1.5	0.3
banyak_kejadian_banjir_2018_2019	−1.1	1.5	0.5
banyak_kejadian_banjir_bandang_2018_2019	−0.3	4.0	−0.3
banyak_kejadian_kebakaran_hutan_dan_lahan_2018_2019	−0.3	4.1	−0.3
banyak_kejadian_kekeringan_lahan_2018_2019	−0.4	3.3	−0.4
banyak_kejadian_tanah_longsor_2018_2019	−0.8	1.8	−0.8
buffer_to_500m_irigated_land	−0.7	2.1	−0.7
distance_to_burned_area	−2.5	3.6	−0.1
distance_to_commodity_processing_factory	−3.4	2.2	0.2
distance_to_deforestation	−2.4	2.2	0.0
distance_to_forest	−4.4	2.0	0.1
distance_to_plantation	−3.1	2.9	0.1
distance_to_plantation_concession	−4.4	0.6	0.3
distance_to_river	−1.9	4.6	−0.1
distance_to_road	−3.7	2.9	−0.1
erosion_risk_t_ha_1_yr_1	−8.3	1.1	0.2
indeks_bahaya_banjir	−2.0	1.2	0.3
indeks_bahaya_longsor	−1.5	1.1	0.4
jumlah_sistem_peringatan_dini_bencana_alam	−2.7	2.8	0.0
jumlah_warga_penderita_gizi_buruk_marasmus_dan_kwashiorkor_pada_tahun_2018	−0.9	1.8	−0.9
korban_jiwa_banjir_2018_2019	−0.2	5.4	−0.2
korban_jiwa_banjir_bandang_2018_2019	−0.1	8.7	−0.1
korban_jiwa_kekeringan_lahan_2018_2019	−0.1	17.6	−0.1
korban_jiwa_tanah_longsor_2018_2019	−0.1	10.1	−0.1
percentage_deforestation_area_size	−0.9	2.6	−0.3
percentage_of_agricultural_area_small_holder_in_the_village	−3.2	1.0	0.3
percentage_of_forested_area_in_the_sub_district	−1.1	1.6	0.0
percentage_of_plantation_area_per_sub_district	−1.8	2.2	0.0
percentage_of_shrubland_in_the_sub_district	−0.2	6.6	−0.2
percentage_of_water_area_compared_to_sub_district_area	−0.2	11.6	−0.2
persentase_sistem_peringatan_dini_bencana_alam	−2.7	3.2	0.0
prec_change	−2.8	2.0	0.1
rasio_40pers_ekon_rendah_indv	−4.3	2.4	0.1
rasio_40pers_ekon_rendah_rt	−4.1	2.3	0.1
rasio_elektrifikasi	−8.7	0.5	0.4
rasio_embung_di_kecamatan	−1.2	1.4	0.6
rasio_faskes_1	−13.8	2.2	0.1
rasio_minimarket_swalayan	−1.4	0.9	0.6
rasio_pasar	−0.5	16.8	−0.1
rasio_pasar_desa_pasar_hewan_pelelangan_ikan_pelelangan_hasil_pertanian_dll	−0.8	1.6	−0.8
rasio_pt	−0.5	2.2	−0.5
rasio_rs	−0.5	2.4	−0.5
rasio_sekolah_tinggi_sma_sederajat	−2.0	2.8	−0.1
rasio_warga_penderita_gizi_buruk_marasmus_dan_kwashiorkor_pada_tahun_2018	−0.9	1.4	−0.9
temp_change	−7.8	0.4	0.1
total_kk_berdasarkan_pengguna_dan_non_pengguna_listrik	−2.9	2.9	0.1

Code

## Boxplot
# Histograms
# boxplot(df_pre_pca)

3.1 Density plots

4 PCA Analysis

Code

# Perform PCA
pca_result <- prcomp(df_pre_pca)

Code

# Assuming pca_result is your prcomp object
pca_summary <- summary(pca_result)$importance |> round(digits = 2)



# Convert to tibble and remove row names
pca_summary_tibble <- tibble::rownames_to_column(as.data.frame(pca_summary), var = "Components")

# Create gt table
pca_summary_tibble|>  
  gt()|>
  tab_header(
    title = "Principal Component Analysis Summary",
    subtitle = "Importance of components") |> 
    opt_align_table_header(align = "left")

Principal Component Analysis Summary
Importance of components
Components	PC1	PC2	PC3	PC4	PC5	PC6	PC7	PC8	PC9	PC10	PC11	PC12	PC13	PC14	PC15	PC16	PC17	PC18	PC19	PC20	PC21	PC22	PC23	PC24	PC25	PC26	PC27	PC28	PC29	PC30	PC31	PC32	PC33	PC34	PC35	PC36	PC37	PC38	PC39	PC40	PC41	PC42	PC43	PC44	PC45	PC46	PC47	PC48	PC49
Standard deviation	2.83	2.07	2.01	1.75	1.60	1.44	1.34	1.29	1.16	1.11	1.08	1.06	1.03	1.02	0.99	0.96	0.94	0.90	0.89	0.88	0.86	0.85	0.83	0.78	0.75	0.74	0.70	0.67	0.66	0.61	0.61	0.59	0.56	0.53	0.50	0.49	0.47	0.42	0.40	0.36	0.33	0.3	0.26	0.23	0.16	0.1	0.05	0.02	0
Proportion of Variance	0.17	0.09	0.08	0.06	0.05	0.04	0.04	0.03	0.03	0.03	0.02	0.02	0.02	0.02	0.02	0.02	0.02	0.02	0.02	0.02	0.02	0.01	0.01	0.01	0.01	0.01	0.01	0.01	0.01	0.01	0.01	0.01	0.01	0.01	0.01	0.00	0.00	0.00	0.00	0.00	0.00	0.0	0.00	0.00	0.00	0.0	0.00	0.00	0
Cumulative Proportion	0.17	0.26	0.34	0.40	0.46	0.50	0.54	0.57	0.60	0.63	0.65	0.67	0.70	0.72	0.74	0.76	0.77	0.79	0.81	0.82	0.84	0.85	0.87	0.88	0.89	0.90	0.92	0.92	0.93	0.94	0.95	0.96	0.96	0.97	0.97	0.98	0.98	0.99	0.99	0.99	0.99	1.0	1.00	1.00	1.00	1.0	1.00	1.00	1

4.1 The Scree Plot

A scree plot visualizes the proportion of variance explained by each PC. The first few PCs are the main contributors, while the rest have minimal influence.

Code

# Visualize the PCA result using a scree plot to see the variance explained by each principal component
plot(pca_result, type = "l", main = "Scree Plot")

4.2 A Look at Loadings

Loadings in PCA reveal how original variables influence each Principal Component. High absolute values indicate strong influence, while the sign indicates the direction. Understanding these can uncover underlying themes, such as climate factors.

4.2.0.1 The importance of the factors for each principal component

Code

# Extract the loadings for the desired number of principal components
num_pc <- 5
loadings <- pca_result$rotation[, 1:num_pc]

# Function to plot ordered loadings
plot_ordered_loadings <- function(loadings, pc_num) {
  ordered_indices <- order(-abs(loadings[, pc_num]), decreasing = TRUE)
  
  # Determine the colours based on the sign of the values
  bar_colours <- ifelse(loadings[ordered_indices, pc_num] < 0, "red", "blue")
  
  barplot(abs(loadings[ordered_indices, pc_num]), horiz = TRUE,
          main = paste("Loadings for PC", pc_num),
          names.arg = rownames(loadings)[ordered_indices],
          las = 1, cex.names = 0.7, xlim = c(0, 0.5), col = bar_colours)
}

# Set up the plotting area with adjusted margins
par(mar = c(5, 25, 4, 2))

# Loop over each principal component and plot
for (i in 1:num_pc) {
  plot_ordered_loadings(loadings, i)
}

To identify the factors that are consistently least influential across the first three principal components, we can look at the absolute values of the loadings. Factors with small absolute loadings are less influential. Knowledge of the specific field aids in interpreting PCs. Principal Components can be complex and may resist straightforward interpretation.

5 Classifying Data with K-Means Clustering

5.0.1 Step 1: Selecting the Principal Components

Start by using the top five Principal Components from PCA, which capture the core variances and correlations in your data.

Code

# Extract the first five principal components
selected_components <- pca_result$x[, 1:5]

5.0.2 Step 2: Determine the Number of Clusters

Select the optimal number of clusters (k) using methods like the Elbow Method or Silhouette Analysis.

5.0.2.1 Elbow Method

The Elbow Method involves running k-means clustering for a range of \(k\) values and plotting the total within-cluster sum of squares. The “elbow” of the plot represents an optimal value for \(k\) (a balance between precision and computational cost).

Code

# Compute total within-cluster sum of squares for different k values
set.seed(45)
wss <- sapply(1:10, function(k) {
  kmeans(selected_components, centers = k)$tot.withinss
})

# Plot the total within-cluster sum of squares
plot(1:10, wss, type = "b", xlab = "Number of Clusters", ylab = "Total Within-Cluster Sum of Squares",
     main = "Elbow Method")

based on the numbers, we might consider the point where the decrease starts to slow down, which could be around \(k\)= 4 or \(k\)=5.

5.0.2.2 Silhouette Analysis

Silhouette Analysis measures how similar an object is to its own cluster compared to other clusters. The silhouette score ranges from -1 to 1, where a high value indicates that the object is well matched to its own cluster and poorly matched to neighboring clusters.

Code

library(cluster)

# Compute silhouette scores for different k values
set.seed(45)
silhouette_scores <- sapply(2:10, function(k) {
  cluster_result <- kmeans(selected_components, centers = k)
  silhouette_avg <- mean(silhouette(cluster_result$cluster, dist(selected_components))[, "sil_width"])
  silhouette_avg
})

# Plot the silhouette scores
plot(2:10, silhouette_scores, type = "b", xlab = "Number of Clusters", ylab = "Average Silhouette Width",
     main = "Silhouette Analysis")

The maximum silhouette score corresponds to 5 clusters (since the first value represents \(k\)=2)

5.0.3 Step 3: Applying K-Means Algorithm

Utilize the k-means algorithm to divide the data into k clusters, focusing on the first three PCs. In R, this can be done with:

Code

# Choose the number of clusters
k <- 5

# Perform k-means clustering
set.seed(45)
kmeans_result <- kmeans(selected_components, centers = k)

5.0.4 Step 4: Interpret the Clusters

Investigate each cluster to understand the common traits within them. Interpretation requires a blend of data analysis and domain-specific knowledge.

Code

library(ggplot2)

# Create a data frame for plotting
plot_data <- data.frame(selected_components, cluster = as.factor(kmeans_result$cluster))

# Plot the first two principal components and color by cluster
ggplot(plot_data, aes(x = PC1, y = PC2, color = cluster)) +
  geom_point() +
  labs(title = "K-means Clustering on First Two Principal Components") +
  theme_minimal()

Code

# Plot the first two principal components and color by cluster
ggplot(plot_data, aes(x = PC1, y = PC3, color = cluster)) +
  geom_point() +
  labs(title = "K-means Clustering on First and Third Principal Components") +
  theme_minimal()

An interactive 3D scatter plot below shows the first three principal components, colored by cluster. We can rotate the plot to view it from different angles, and you can hover over the points to see additional information.

Code

# Load the plotly package
library(plotly)

Attaching package: 'plotly'

The following object is masked from 'package:ggplot2':

    last_plot

The following object is masked from 'package:stats':

    filter

The following object is masked from 'package:graphics':

    layout

Code

names_kab_kec<- scaled_df_complete_temp |> 
  select(c(nmkab, nmkec))

# Create a data frame for plotting
plot_data <- data.frame(selected_components, cluster = as.factor(kmeans_result$cluster)) |> bind_cols(names_kab_kec)

# Create the 3D scatter plot
plot_3d <- plot_ly(
  data = plot_data,
  x = ~ PC1,
  y = ~ PC2,
  z = ~ PC3,
  color = ~ cluster,
  type = "scatter3d",
  text = ~ paste("Kab./Kota:", nmkab, "<br>Kecamatan:", nmkec),
  mode = "markers"
) 
# Show the plot
plot_3d

5.0.5 Step 5: Visualise the clusters into a map

Code

library(terra)
library(sf)
# Read the shapefile
desa <- st_read("data/INDO_DESA_2019/INDO_DESA_2019.shp")

Reading layer `INDO_DESA_2019' from data source 
  `D:\OneDrive - CIFOR-ICRAF\Documents\GitHub\vulnerability-typology-map\data\INDO_DESA_2019\INDO_DESA_2019.shp' 
  using driver `ESRI Shapefile'
Simple feature collection with 84091 features and 12 fields
Geometry type: MULTIPOLYGON
Dimension:     XY
Bounding box:  xmin: 95.00971 ymin: -11.00766 xmax: 141.02 ymax: 6.076809
Geodetic CRS:  WGS 84

Code

# Filter based on the 'kdprov' attribute
desa_sulsel <- desa |> filter(kdprov %in% 73)
desa_sulsel <- desa_sulsel |> dplyr::select(-c("kddesa", "iddesa"))
desa_sulsel_id_kec <- desa_sulsel |> select(nmkab,nmkec,kdprov,kdkab,kdkec) |> 
  mutate(idkec_dum = paste0(kdprov,kdkab,kdkec, "a") )
rm(desa)

# add the cluster attribute to the desa_sulsel object
cluster_data<- scaled_df_complete_temp |> select(-c(nmkab, nmkec ,nmprov ,  sumber, kdprov,kdkab,kdkec)) |> 
  dplyr::select(1:9) |> bind_cols(tibble (cluster = kmeans_result$cluster))

clusters_sulsel<- desa_sulsel_id_kec |> left_join(cluster_data, by = "idkec_dum")

# Write the sf object to a shapefile
st_write(clusters_sulsel, "output/tipologi_5_kelas.shp", append = TRUE)

Updating layer `tipologi_5_kelas' to data source `output/tipologi_5_kelas.shp' using driver `ESRI Shapefile'
Updating existing layer tipologi_5_kelas
Writing 3053 features with 15 fields and geometry type Multi Polygon.

Code

# # Plot the SpatVector object, using the 'cluster' attribute for the fill color
# plot(desa_sulsel, "cluster", col=c("#E69F00", "#CC79A7", "#009E73", "#F0E442", "#0072B2"), lwd=0.1) # Assuming we have 5 clusters

library(leaflet)
# Create a color palette for the 'cluster' variable
pal <- colorFactor(palette = "Set1", domain = clusters_sulsel$cluster)

# Constructing the label string first
clusters_sulsel$label_content <- with(clusters_sulsel, 
                                      paste0("<strong>Kabupaten:</strong> ", nmkab, "<br>",
                                             "<strong>Kecamatan:</strong> ", nmkec, "<br>",
                                             "<strong>Cluster:</strong> ", cluster)) |> lapply(htmltools::HTML)


# Create the leaflet map with HTML-rendered labels
leaflet(clusters_sulsel) |> 
  addProviderTiles(providers$OpenStreetMap)|>
  addPolygons(
    fillColor = ~pal(cluster),
    weight = 0.5,
    opacity = 1,
    color = "white",
    dashArray = "3",
    fillOpacity = 0.7,
    highlight = highlightOptions(
      weight = 5,
      color = "#666",
      dashArray = "",
      fillOpacity = 0.7,
      bringToFront = TRUE
    ),
    label = ~label_content,
    labelOptions = labelOptions(
      noHide = FALSE,
      direction = 'auto'
    )
  )|>
  addLegend(pal = pal, values = ~cluster, title = "Cluster")

6 Warning

• Lack of Data Understanding: The analysis was conducted without in-depth knowledge of the data, so the results should be interpreted cautiously.